Optimal and Robust Designs for Regression

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The main objective of this research program is to understand how the nature of designs of experiments affects the results of estimation, prediction, and extrapolation in regression for various models assumed with or most likely without accuracy and to develop theory and methods of constructing regression designs that provide efficient results with optimized balance between precision in estimates and protection from possible model departures.****The areas of generalized linear fixed models (GLM), generalized linear mixed models (GLMM), accelerated life testing (ALT), and quantile regression have attracted much research activity. Significant results on optimal and robust designs for GLM, GLMM, and ALT have been obtained under my current grant. Recently, we have also achieved important results for analysis of weighted quantile regression (WQR) but not yet explored its design issue. This proposal aims to primarily build upon design construction for GLM, GLMM, ALT, and innovatively develop theory and methods of design construction for WQR. ****For GLM:***I will continue working on constructing robust design, using newly developed methods, for general GLM with possible overdispersion and inaccuracies in the assumed linear predictor, in model parameter specification, and in the assumed link function.****For GLMM:***Building on my earlier work for constructing optimal design for GLMM, I will explore robust design methods for GLMM with possible misspecified random effects distribution and inaccuracy in the assumed linear predictor. Both model parameter estimation and the Fisher information calculation for GLMM are often challenging, especially when multiple random effects or a multidimensional design space is involved. Hence, I will also investigate the computational issues concerned.****For ALT:***Whereas previous research on optimal and robust design for ALT has mainly focused on parametric models, I plan to construct optimal and robust design for ALT for a commonly used semi-parametric model - a proportional hazard model (PHM). The assumed baseline hazard function in a PHM is often with uncertainty due to the extrapolation nature of ALT and the resulting optimal deigns often depend on PHM parameters. Therefore, I will also construct robust deigns against possible misspecification in the assumed baseline hazard function and in the initial parameter values.****For WQR:***The most important virtue of quantile regression is its capability to make inferences on the entire conditional response distribution. However, there is minimal literature (all considered classical quantile regression) addressing optimal and robust design problems for quantile regression. It has been shown that WQR is an important method to improve the performance of statistical analysis for quantile regression, especially when heteroscedasticity is present. Hence, I will also develop theory and methods of optimal and robust designs for WQR.**