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

模型误定是统计分析中一个非常重要的问题，因为误定模型会导致估计不一致和/或估计效率低下。我的研究计划侧重于建立严格的统计测试和诊断工具的模型误定和发展稳健的估计和推理程序下的模型误定。 在线性回归模型中，通常假设方差齐性。然而，这一假设是违反异方差数据，可能会出现在许多应用，包括经济学，环境科学，和其他实质性领域。我的工作集中在开发强大的测试，以确定协变量有助于异方差性。我提出的方法可以应用于分析各种类型的响应变量，包括连续结果，删失生存结果和时间序列。 在风险预测中，如果在传统预测因子之上添加新的预测因子，则量化预测精度的提高是重要的。由于简单的工作模型，这可能是错误的，被用来作为预测模型，以近似复杂的潜在概率机制，我将开发一个框架，强大的估计和推理程序，以改善新的预测模型下的错误。此外，这一框架将考虑到实际的复杂性，如存在竞争风险的情况，或由于新预测因素的高测量成本而采用复杂抽样设计的情况。

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.