A hybrid deep learning framework for air quality prediction with spatial autocorrelation during the COVID-19 pandemic.

China implemented a strict lockdown policy to prevent the spread of COVID-19 in the worst-affected regions, including Wuhan and Shanghai. This study aims to investigate impact of these lockdowns on air quality index (AQI) using a deep learning framework. In addition to historical pollutant concentrations and meteorological factors, we incorporate social and spatio-temporal influences in the framework. In particular, spatial autocorrelation (SAC), which combines temporal autocorrelation with spatial correlation, is adopted to reflect the influence of neighbouring cities and historical data. Our deep learning analysis obtained the estimates of the lockdown effects as - 25.88 in Wuhan and - 20.47 in Shanghai. The corresponding prediction errors are reduced by about 47% for Wuhan and by 67% for Shanghai, which enables much more reliable AQI forecasts for both cities.

Accurate interval estimation for the risk difference in an incomplete correlated 2 × 2 table: Calf immunity analysis.

Interval estimation with accurate coverage for risk difference (RD) in a correlated 2 × 2 table with structural zero is a fundamental and important problem in biostatistics. The score test-based and Bayesian tail-based confidence intervals (CIs) have good coverage performance among the existing methods. However, as approximation approaches, they have coverage probabilities lower than the nominal confidence level for finite and moderate sample sizes. In this paper, we propose three new CIs for RD based on the fiducial, inferential model (IM) and modified IM (MIM) methods. The IM interval is proven to be valid. Moreover, simulation studies show that the CIs of fiducial and MIM methods can guarantee the preset coverage rate even for small sample sizes. More importantly, in terms of coverage probability and expected length, the MIM interval outperforms other intervals. Finally, a real example illustrates the application of the proposed methods.

A Modified Memetic Algorithm with an Application to Gene Selection in a Sheep Body Weight Study.

Selecting the minimal best subset out of a huge number of factors for influencing the response is a fundamental and very challenging NP-hard problem because the presence of many redundant genes results in over-fitting easily while missing an important gene can more detrimental impact on predictions, and computation is prohibitive for exhaust search. We propose a modified memetic algorithm (MA) based on an improved splicing method to overcome the problems in the traditional genetic algorithm exploitation capability and dimension reduction in the predictor variables. The new algorithm accelerates the search in identifying the minimal best subset of genes by incorporating it into the new local search operator and hence improving the splicing method. The improvement is also due to another two novel aspects: (a) updating subsets of genes iteratively until the no more reduction in the loss function by splicing and increasing the probability of selecting the true subsets of genes; and (b) introducing add and del operators based on backward sacrifice into the splicing method to limit the size of gene subsets. Additionally, according to the experimental results, our proposed optimizer can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms. Moreover, the mutation operator is replaced by it to enhance exploitation capability and initial individuals are improved by it to enhance efficiency of search. A dataset of the body weight of Hu sheep was used to evaluate the superiority of the modified MA against the genetic algorithm. According to our experimental results, our proposed optimizer can obtain a better minimal subset of genes with a few iterations, compared with all considered algorithms including the most advanced adaptive best-subset selection algorithm.

A working likelihood approach for robust regression.

Robust approach is often desirable in presence of outliers for more efficient parameter estimation. However, the choice of the regularization parameter value impacts the efficiency of the parameter estimators. To maximize the estimation efficiency, we construct a likelihood function for simultaneously estimating the regression parameters and the tuning parameter. The "working" likelihood function is deemed as a vehicle for efficient regression parameter estimation, because we do not assume the data are generated from this likelihood function. The proposed method can effectively find a value of the regularization parameter based on the extent of contamination in the data. We carry out extensive simulation studies in a variety of cases to investigate the performance of the proposed method. The simulation results show that the efficiency can be enhanced as much as 40% when the data follow a heavy-tailed distribution, and reaches as high as 468% for the heteroscedastic variance cases compared to the traditional Huber's method with a fixed regularization parameter. For illustration, we also analyzed two datasets: one from a diabetics study and the other from a mortality study.