Energy dynamics affecting the US economy; natural energy investments, carbon emissions, production, exports and GDP per Capita.

This study investigates how carbon dioxide emissions, natural gas, energy consumption, energy investment, coal and crude oil, and per capita exports affected the economic growth of the United States from 1993 to 2023 using the Vector Error Correction (VEC) model. The findings highlight the importance of exports and energy investment in driving both short- and long-term economic growth, while also highlighting interactions between carbon emissions, coal use and crude oil. It was determined that changes in natural gas and exports affected energy investment in the short term, while coal and exports affected natural gas. These results provide valuable information about the dynamics of the American economy and contribute to our understanding of the complex interactions between various factors and their effects on economic growth, offering implications for further research and policy development to promote sustainable economic development.

Exploration of the MCMC Wald test with linear regression.

Recently, Asparouhov and Muthén Structural Equation Modeling: A Multidisciplinary Journal, 28, 1-14, (2021a, 2021b) proposed a variant of the Wald test that uses Markov chain Monte Carlo machinery to generate a chi-square test statistic for frequentist inference. Because the test's composition does not rely on analytic expressions for sampling variation and covariation, it potentially provides a way to get honest significance tests in cases where the likelihood-based test statistic's assumptions break down (e.g., in small samples). The goal of this study is to use simulation to compare the new MCM Wald test to its maximum likelihood counterparts, with respect to both their type I error rate and power. Our simulation examined the test statistics across different levels of sample size, effect size, and degrees of freedom (test complexity). An additional goal was to assess the robustness of the MCMC Wald test with nonnormal data. The simulation results uniformly demonstrated that the MCMC Wald test was superior to the maximum likelihood test statistic, especially with small samples (e.g., sample sizes less than 150) and complex models (e.g., models with five or more predictors). This conclusion held for nonnormal data as well. Lastly, we provide a brief application to a real data example.

A Time-Varying Mixture Integer-Valued Threshold Autoregressive Process Driven by Explanatory Variables.

In this paper, a time-varying first-order mixture integer-valued threshold autoregressive process driven by explanatory variables is introduced. The basic probabilistic and statistical properties of this model are studied in depth. We proceed to derive estimators using the conditional least squares (CLS) and conditional maximum likelihood (CML) methods, while also establishing the asymptotic properties of the CLS estimator. Furthermore, we employed the CLS and CML score functions to infer the threshold parameter. Additionally, three test statistics to detect the existence of the piecewise structure and explanatory variables were utilized. To support our findings, we conducted simulation studies and applied our model to two applications concerning the daily stock trading volumes of VOW.

Omnibus test for restricted mean survival time based on influence function.

The restricted mean survival time (RMST), which evaluates the expected survival time up to a pre-specified time point τ, has been widely used to summarize the survival distribution due to its robustness and straightforward interpretation. In comparative studies with time-to-event data, the RMST-based test has been utilized as an alternative to the classic log-rank test because the power of the log-rank test deteriorates when the proportional hazards assumption is violated. To overcome the challenge of selecting an appropriate time point τ, we develop an RMST-based omnibus Wald test to detect the survival difference between two groups throughout the study follow-up period. Treating a vector of RMSTs at multiple quantile-based time points as a statistical functional, we construct a Wald χ2 test statistic and derive its asymptotic distribution using the influence function. We further propose a new procedure based on the influence function to estimate the asymptotic covariance matrix in contrast to the usual bootstrap method. Simulations under different scenarios validate the size of our RMST-based omnibus test and demonstrate its advantage over the existing tests in power, especially when the true survival functions cross within the study follow-up period. For illustration, the proposed test is applied to two real datasets, which demonstrate its power and applicability in various situations.

Nonlinear effects of public debt on economic growth in Nigeria.

The COVID-19 pandemic induced governments all over the world to momentarily accumulate higher levels of public debt in order to invest in deficit spending and social protection programs to tackle the anticipated economic slump. The Nigerian government has borrowed heavily from domestic and foreign sources in order to resolve the growing budget deficits and return the economy to a sustainable growth trajectory. Previous studies frequently made the incorrect assumption that the relationship between public debt and growth is linear and symmetric, leading to empirical results that is frequently disputed and imprecise. This study's main objective is to examine the asymmetric impact of public debt on economic growth in Nigeria from 1980 to 2020 using the Nonlinear Autoregressive Distributed Lag method. Empirical evidence indicated that external debt have a significant positive and symmetric impact on economic growth in the long and short run, while debt service payment supporting the debt overhang hypothesis activated a symmetric effect that stifle growth. Domestic debt retarded growth asymmetrically in the short term and linearly over the long term. Foreign reserve holding, on the other hand, had an asymmetric long-run influence and a symmetric short-run impact on growth motivation. To mitigate the negative effects of unsustainable public debt, the study advocated for fiscal reforms that effectively reduce deficit financing to keep the level of government debt low and be able to respond robustly to an economic shock, improve domestic revenue generation and infrastructure spending, and strengthen governance practices and institutions.

A Statistical Investigation into the COVID-19 Outbreak Spread.

Objective: Coronavirus-19 (COVID-19) outbreaks have been reported in a range of climates worldwide, including Bangladesh. There is less evidence of a link between the COVID-19 pandemic and climatic variables. This research article's purpose is to examine the relationship between COVID-19 outbreaks and climatic factors in Dhaka, Bangladesh. Methods: The daily time series COVID-19 data used in this study span from May 1, 2020, to April 14, 2021, for the study area, Dhaka, Bangladesh. The Climatic factors included in this study were average temperature, particulate matter ( P M 2 . 5 ), humidity, carbon emissions, and wind speed within the same timeframe and location. The strength and direction of the relationship between meteorological factors and COVID-19 positive cases are examined using the Spearman correlation. This study examines the asymmetric effect of climatic factors on the COVID-19 pandemic in Dhaka, Bangladesh, using the Nonlinear Autoregressive Distributed Lag (NARDL) model. Results: COVID-19 widespread has a substantial positive association with wind speed (r = .781), temperature (r = .599), and carbon emissions (r = .309), whereas P M 2 . 5 (r = -.178) has a negative relationship at the 1% level of significance. Furthermore, with a 1% change in temperature, the incidence of COVID-19 increased by 1.23% in the short run and 1.53% in the long run, with the remaining variables remaining constant. Similarly, in the short-term, humidity was not significantly related to the COVID-19 pandemic. However, in the long term, it increased 1.13% because of a 1% change in humidity. The changes in PM2.5 level and wind speed are significantly associated with COVID-19 new cases after adjusting population density and the human development index.

A series of two-sample non-parametric tests for quantile residual life time.

Quantile residual lifetime (QRL) is of significant interest in many clinical studies as an easily interpretable quantity compared to other summary measures of survival distributions. In cancer or other chronic diseases, treatments are often compared based on the distributions or quantiles of the residual lifetime. Thus a common problem of interest is to test the equality of the QRL between two populations. In this paper, we propose two classes of tests to compare two QRLs; one class is based on the difference between two estimated QRLs, and the other is based on the estimating function of the QRL, where the estimated QRL from one sample is plugged into the QRL-estimating-function of the other sample. We outline the asymptotic properties of these test statistics. Simulation studies demonstrate that the proposed tests produced Type I errors closer to the nominal level and are superior to some existing tests based on both Type I error and power. Our proposed test statistics are also computationally less intensive and more straightforward compared to tests based on the confidence intervals. We applied the proposed methods to a randomized multicenter phase III trial for breast cancer patients.

Power Analysis for the Wald, LR, Score, and Gradient Tests in a Marginal Maximum Likelihood Framework: Applications in IRT.

The Wald, likelihood ratio, score, and the recently proposed gradient statistics can be used to assess a broad range of hypotheses in item response theory models, for instance, to check the overall model fit or to detect differential item functioning. We introduce new methods for power analysis and sample size planning that can be applied when marginal maximum likelihood estimation is used. This allows the application to a variety of IRT models, which are commonly used in practice, e.g., in large-scale educational assessments. An analytical method utilizes the asymptotic distributions of the statistics under alternative hypotheses. We also provide a sampling-based approach for applications where the analytical approach is computationally infeasible. This can be the case with 20 or more items, since the computational load increases exponentially with the number of items. We performed extensive simulation studies in three practically relevant settings, i.e., testing a Rasch model against a 2PL model, testing for differential item functioning, and testing a partial credit model against a generalized partial credit model. The observed distributions of the test statistics and the power of the tests agreed well with the predictions by the proposed methods in sufficiently large samples. We provide an openly accessible R package that implements the methods for user-supplied hypotheses.

Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic.

Mediation analysis draws increasing attention in many research areas such as economics, finance and social sciences. In this paper, we propose new statistical inference procedures for high dimensional mediation models, in which both the outcome model and the mediator model are linear with high dimensional mediators. Traditional procedures for mediation analysis cannot be used to make statistical inference for high dimensional linear mediation models due to high-dimensionality of the mediators. We propose an estimation procedure for the indirect effects of the models via a partially penalized least squares method, and further establish its theoretical properties. We further develop a partially penalized Wald test on the indirect effects, and prove that the proposed test has a χ 2 limiting null distribution. We also propose an F -type test for direct effects and show that the proposed test asymptotically follows a χ 2 -distribution under null hypothesis and a noncentral χ 2 -distribution under local alternatives. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed tests and compare their performance with existing ones. We further apply the newly proposed statistical inference procedures to study stock reaction to COVID-19 pandemic via an empirical analysis of studying the mediation effects of financial metrics that bridge company's sector and stock return.

Services as a Determinant of Botswana's Economic Sustainability.

In 2015, the services sector contributed about 58 percent to the gross domestic product (GDP) in Sub-Saharan Africa (SSA), which was a significant increase from the 47.6 percent observed in 2005, and a shift from the mining, agriculture, and manufacturing sector. This increase calls to support services as the catalyst for sustained economic development as indicated by the structural transformation and modernization theories. The main objective of this paper was to examine the relationship between and the impact of services on the economic development in Botswana and make recommendations on how Botswana can apply well-directed policies to improve its services sector and diversify its impact on other sectors and GDP, making it less reliant on mining which is vulnerable to price volatilities. The paper applied econometric modeling and results of the Autoregressive-Distributed Lag (ARDL) Bounds test for cointegration indicate that services and other industries services, agriculture, industry, mining, and investment impact GDP over the short and long run. These variables impacted GDP and converged to equilibrium at the speed of 46.89 percent, with a percent change in services in the short and long run impacting GDP by 0.328 and 0.241 percentages, respectively, and the outcome of the Wald test indicated causality from services to GDP growth. The services sectors have contributed over 40 percent to the country's GDP from 1995 to the present, though the sectors have not gone without challenges with limitations such as limited infrastructure development; poverty and inequality; unemployment of over 20 percent; disease, which has dampened productivity; and lack of proper governance and accountability, which has created a habitat for an increase in cases of corruption in state and private entities. The findings of the study with the lessons learned from other studies with similar findings recommend that the government of Botswana should formulate suitable policies and strategies for services diversification. This is by expanding the market for the sector in areas such as tourism that were impacted by the COVID-19 pandemic, escalating investments by instituting strategies to attract and grow domestic and foreign investments, and improve on management of institutions and resources.

Testing latent class of subjects with structural zeros in negative binomial models with applications to gut microbiome data.

Human microbiome research has become a hot-spot in health and medical research in the past decade due to the rapid development of modern high-throughput. Typical data in a microbiome study consisting of the operational taxonomic unit counts may have over-dispersion and/or structural zero issues. In such cases, negative binomial models can be applied to address the over-dispersion issue, while zero-inflated negative binomial models can be applied to address both issues. In practice, it is essential to know if there is zero-inflation in the data before applying negative binomial or zero-inflated negative binomial models because zero-inflated negative binomial models may be unnecessarily complex and difficult to interpret, or may even suffer from convergence issues if there is no zero-inflation in the data. On the other hand, negative binomial models may yield invalid inferences if the data does exhibit excessive zeros. In this paper, we develop a new test for detecting zero-inflation resulting from a latent class of subjects with structural zeros in a negative binomial regression model by directly comparing the amount of observed zeros with what would be expected under the negative binomial regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Intensive simulation studies are conducted to investigate the performance of the new test and compare it with the classical Wald, likelihood ratio, and score tests. The tests are also applied to human gut microbiome data to test latent class in microbial genera.

Distributed Target Detection in Unknown Interference.

Interference can degrade the detection performance of a radar system. To overcome the difficulty of target detection in unknown interference, in this paper we model the interference belonging to a subspace orthogonal to the signal subspace. We design three effective detectors for distributed target detection in unknown interference by adopting the criteria of the generalized likelihood ratio test (GLRT), the Rao test, and the Wald test. At the stage of performance evaluation, we illustrate the detection performance of the proposed detectors in the presence of completely unknown interference (not constrained to lie in the above subspace). Numerical examples indicate that the proposed GLRT and Wald test can provide better detection performance than the existing detectors.

Inference in Functional Linear Quantile Regression.

In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regression parameter function that varies with the level of quantile. The objective is to test that the regression parameter is constant across several quantile levels of interest. The parameter function is estimated by combining ideas from functional principal component analysis and quantile regression. An adjusted Wald testing procedure is proposed for this hypothesis of interest, and its chi-square asymptotic null distribution is derived. The testing procedure is investigated numerically in simulations involving sparse and noisy functional covariates and in a capital bike share data application. The proposed approach is easy to implement and the R code is published online at https://github.com/xylimeng/fQR-testing.

Revisiting the Wald Test in Small Case-Control Studies With a Skewed Covariate.

The Wald test is routinely used in case-control studies to test for association between a covariate and disease. However, when the evidence for association is high, the Wald test tends to inflate small P values as a result of the Hauck-Donner effect (HDE). Here, we investigate the HDE in the context of genetic burden, both with and without additional covariates. First, we examine the burden-based P values in the absence of association using whole-exome sequence data from 1000 Genomes Project reference samples (n = 54) and selected preterm infants with neonatal complications (n = 74). Our careful analysis of the burden-based P values shows that the HDE is present and that the cause of the HDE in this setting is likely a natural extension of the well-known cause of the HDE in 2 × 2 contingency tables. Second, in a reanalysis of real data, we find that the permutation test provides increased power over the Wald, Firth, and likelihood ratio tests, which agrees with our intuition since the permutation test is valid for any sample size and since it does not suffer from the HDE. Therefore, we propose a powerful and computationally efficient permutation-based approach for the analysis and reanalysis of small case-control association studies.

Genetic association tests in family samples for multi-category phenotypes.

BACKGROUND: Advancements in statistical methods and sequencing technology have led to numerous novel discoveries in human genetics in the past two decades. Among phenotypes of interest, most attention has been given to studying genetic associations with continuous or binary traits. Efficient statistical methods have been proposed and are available for both types of traits under different study designs. However, for multinomial categorical traits in related samples, there is a lack of efficient statistical methods and software. RESULTS: We propose an efficient score test to analyze a multinomial trait in family samples, in the context of genome-wide association/sequencing studies. An alternative Wald statistic is also proposed. We also extend the methodology to be applicable to ordinal traits. We performed extensive simulation studies to evaluate the type-I error of the score test, Wald test compared to the multinomial logistic regression for unrelated samples, under different allele frequency and study designs. We also evaluate the power of these methods. Results show that both the score and Wald tests have a well-controlled type-I error rate, but the multinomial logistic regression has an inflated type-I error rate when applied to family samples. We illustrated the application of the score test with an application to the Framingham Heart Study to uncover genetic variants associated with diabesity, a multi-category phenotype. CONCLUSION: Both proposed tests have correct type-I error rate and similar power. However, because the Wald statistics rely on computer-intensive estimation, it is less efficient than the score test in terms of applications to large-scale genetic association studies. We provide computer implementation for both multinomial and ordinal traits.

A comparison of hypothesis tests for homogeneity in meta-analysis with focus on rare binary events.

Analysis of rare binary events is an important problem for biomedical researchers. Due to the sparsity of events in such problems, meta-analysis that integrates information across multiple studies can be applied to increase the efficiency of statistical inference. Although it is critical to examine whether the effect sizes are homogeneous across all studies, a comprehensive review of homogeneity tests has been lacking, and in particular, no attention has been paid to infrequent dichotomous outcomes. We systematically review statistical methods for homogeneity testing. By conducting an extensive simulation analysis and two case studies, we examine the performance of 30 tests in meta-analysis of rare binary outcomes. When using log-odds ratio as the association measure, our simulation results suggest that there is no uniform winner. However, we recommend the test proposed by Kulinskaya and Dollinger (BMC Med Res Methodol, 2015, 15), which uses a gamma distribution to approximate the null distribution, for its generally good performance; for very rare events coupled with small within-study sample sizes, in addition to the Kulinskaya-Dollinger test, we further recommend the conditional score test based on the random-effects hypergeometric model proposed by Liang and Self (Biometrika, 1985, 72:353-358). One should be cautious about the use of the Wald tests, the Lipsitz tests (Biometrics, 1998, 54:148-160), and tests proposed by Bhaumik et al (J Am Stat Assoc, 2012, 107:555-567).

Type I error control for cluster randomized trials under varying small sample structures.

BACKGROUND: Linear mixed models (LMM) are a common approach to analyzing data from cluster randomized trials (CRTs). Inference on parameters can be performed via Wald tests or likelihood ratio tests (LRT), but both approaches may give incorrect Type I error rates in common finite sample settings. The impact of different combinations of cluster size, number of clusters, intraclass correlation coefficient (ICC), and analysis approach on Type I error rates has not been well studied. Reviews of published CRTs find that small sample sizes are not uncommon, so the performance of different inferential approaches in these settings can guide data analysts to the best choices. METHODS: Using a random-intercept LMM stucture, we use simulations to study Type I error rates with the LRT and Wald test with different degrees of freedom (DF) choices across different combinations of cluster size, number of clusters, and ICC. RESULTS: Our simulations show that the LRT can be anti-conservative when the ICC is large and the number of clusters is small, with the effect most pronouced when the cluster size is relatively large. Wald tests with the between-within DF method or the Satterthwaite DF approximation maintain Type I error control at the stated level, though they are conservative when the number of clusters, the cluster size, and the ICC are small. CONCLUSIONS: Depending on the structure of the CRT, analysts should choose a hypothesis testing approach that will maintain the appropriate Type I error rate for their data. Wald tests with the Satterthwaite DF approximation work well in many circumstances, but in other cases the LRT may have Type I error rates closer to the nominal level.

Detecting Differential Item Functioning Using Multiple-Group Cognitive Diagnosis Models.

This study proposes a multiple-group cognitive diagnosis model to account for the fact that students in different groups may use distinct attributes or use the same attributes but in different manners (e.g., conjunctive, disjunctive, and compensatory) to solve problems. Based on the proposed model, this study systematically investigates the performance of the likelihood ratio (LR) test and Wald test in detecting differential item functioning (DIF). A forward anchor item search procedure was also proposed to identify a set of anchor items with invariant item parameters across groups. Results showed that the LR and Wald tests with the forward anchor item search algorithm produced better calibrated Type I error rates than the ordinary LR and Wald tests, especially when items were of low quality. A set of real data were also analyzed to illustrate the use of these DIF detection procedures.

A new statistical test for latent class in censored data due to detection limit.

Biomarkers of interest in urine, serum, or other biological matrices often have an assay limit of detection. When concentration levels of the biomarkers for some subjects fall below the limit, the measures for those subjects are censored. Censored data due to detection limits are very common in public health and medical research. If censored data from a single exposure group follow a normal distribution or follow a normal distribution after some transformations, Tobit regression models can be applied. Given a Tobit regression model and a detection limit, the proportion of censored data can be determined. However, in practice, it is common that the data can exhibit excessive censored observations beyond what would be expected under a Tobit regression model. One common cause is heterogeneity of the study population, that is, there exists a subpopulation who lack such biomarkers and their values are always under the detection limit, and hence are censored. In this article, we develop a new test for testing such latent class under a Tobit regression model by directly comparing the amount of observed censored data with what would be expected under the Tobit regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Simulation studies are conducted to investigate the performance of the new test and compare the new one with the existing ones including the Wald test, likelihood ratio test, and score test. Two real data examples are also included for illustrative purpose.

Sequentially Estimating the Approximate Conditional Mean Using Extreme Learning Machines.

This study examined the extreme learning machine (ELM) applied to the Wald test statistic for the model specification of the conditional mean, which we call the WELM testing procedure. The omnibus test statistics available in the literature weakly converge to a Gaussian stochastic process under the null that the model is correct, and this makes their application inconvenient. By contrast, the WELM testing procedure is straightforwardly applicable when detecting model misspecification. We applied the WELM testing procedure to the sequential testing procedure formed by a set of polynomial models and estimate an approximate conditional expectation. We then conducted extensive Monte Carlo experiments to evaluate the performance of the sequential WELM testing procedure and verify that it consistently estimates the most parsimonious conditional mean when the set of polynomial models contains a correctly specified model. Otherwise, it consistently rejects all the models in the set.