Grant: Discovery Grants Program - Individual

Different types of data such as count, binary, censored, and longitudinal often arise in public health, biology, epidemiology, and social sciences. These data may be low dimensional (when the number of observations n is greater than the number of predictors p) or high dimensional (n >n, partial linear models, and generalized linear mixed models. Penalty methods, such as LASSO, Adaptive LASSO, SCAD, and GLMMLasso alternative to shrinkage for variable selection and parameter estimation simultaneously have emerged in the past decades. These methods heavily depend on tuning parameters. The shrinkage method, on the other hand does not depend on the tuning parameters, and it may be an alternative to penalty methods. The asymptotic properties of the shrinkage and pretest estimators including the derivation of asymptotic biases and risks will be established. Finally I will compare the relative performance of the penalty estimator the pretest and shrinkage estimators in terms of simulated relative efficiency. It is expected that the proposed research results will provide an efficient method to researchers and practitioners for inference after model selection and in assessing the predictive ability and interpretability of the model.