Statistical Methods for Model Diagnosis and Robust Statistical Procedures under Model Misspecification

点击翻译按钮获取中文摘要

Model misspecification is a problem of great importance in statistical analysis as misspecified models can lead to estimation inconsistency and/or estimation inefficiency. My research program focuses on establishing rigorous statistical tests and diagnostic tools for model misspecification and developing robust estimation and inference procedures under model misspecification. In linear regression models, it is common to assume homogeneous variances. However, this assumption is violated in heteroscedastic data that may arise in many applications including economics, environmental sciences, and other substantive areas. My work is centered on developing powerful tests for identifying covariates contributing to heteroscedasticity. My proposed method can be applied to the analysis of various types of response variables, including continuous outcomes, censored survival outcomes, and time series. In risk prediction, it is important to quantify the improvement in prediction accuracy if new predictors are added on top of traditional predictors. Since simple working models, which are likely misspecified, are used as the prediction model to approximate sophisticated underlying probabilistic mechanisms, I will develop a framework of robust estimation and inference procedures for the improvement of the new predictors under model misspecification. In addition, this framework will allow for practical complications such as situations where competing risks are present, or situations where complex sampling designs are employed due to high measurement costs of the new predictors.