Modeling the Dynamics of the U.S. Healthcare Expenditure Using a Hyperbolastic Function.

In this paper, we investigate the dynamics of the U.S. national healthcare expenditures from 1960 to 2011. The data were obtained from the U.S. Department of Health and Human Services, Center for Medicare and Medicaid Services. The analytical method allows extracting the long-run deterministic trend from the cyclical and the random components. The long-run trend is estimated using six classical growth models and three more recent growth curves called Hyperbolastic growth models of types I, II, and III, denoted by H1, H2, and H3, respectively. The statistical results indicate that the H1 model provides the best fit of the data. The study is complemented by a mathematical analysis of the deterministic long-run component of the national healthcare expenditure (NHE) as modeled by H1. This analysis is performed by examining the behavior of the absolute growth rate (pace of increase curve), the relative growth rate, and the acceleration of the U.S. NHE over the 52-year time frame. To the best of our knowledge, this paper provides the first application of Hyperbolastic models to economics data. This study can be used by researchers and policy makers as a descriptive as well as a predictive tool.

A New Robust Method for Nonlinear Regression.

BACKGROUND: When outliers are present, the least squares method of nonlinear regression performs poorly. The main purpose of this paper is to provide a robust alternative technique to the Ordinary Least Squares nonlinear regression method. This new robust nonlinear regression method can provide accurate parameter estimates when outliers and/or influential observations are present. METHOD: Real and simulated data for drug concentration and tumor size-metastasis are used to assess the performance of this new estimator. Monte Carlo simulations are performed to evaluate the robustness of our new method in comparison with the Ordinary Least Squares method. RESULTS: In simulated data with outliers, this new estimator of regression parameters seems to outperform the Ordinary Least Squares with respect to bias, mean squared errors, and mean estimated parameters. Two algorithms have been proposed. Additionally and for the sake of computational ease and illustration, a Mathematica program has been provided in the Appendix. CONCLUSION: The accuracy of our robust technique is superior to that of the Ordinary Least Squares. The robustness and simplicity of computations make this new technique more appropriate and useful tool for the analysis of nonlinear regressions.

Robust Logistic and Probit Methods for Binary and Multinomial Regression.

In this paper we introduce new robust estimators for the logistic and probit regressions for binary, multinomial, nominal and ordinal data and apply these models to estimate the parameters when outliers or inluential observations are present. Maximum likelihood estimates don't behave well when outliers or inluential observations are present. One remedy is to remove inluential observations from the data and then apply the maximum likelihood technique on the deleted data. Another approach is to employ a robust technique that can handle outliers and inluential observations without removing any observations from the data sets. The robustness of the method is tested using real and simulated data sets.