Robust Inference for Dependent Data

The investigator proposes two different approaches to address a broad variety of parametric and nonparametric inference problems under unknown nonstationarity and dependence. The first approach explores several self-normalization based methods to avoid the estimation of complicated limiting variance function. The proposed methodology can be used to address various nonparametric inference problems, such as nonparametric mean regression, quantile regression, and nonparametric inference for locally stationary processes. The second approach proposes a random perturbation based framework for robust inferences. The idea is to suppress the unknown nonstationarity and dependence at the cost of inflated noise level. The proposed random perturbation method is robust against unknown nonstationarity and dependence, and it is generally applicable for univariate and multivariate parameter inferences, conditional mean regression inference, nonparametric inference, change-point analysis, and nonlinear regression.

Many practical data exhibit complicated time-varying pattern and dependence. Without taking into account such unknown nonstationarity and serial dependence, existing statistical methods developed for independent data or stationary data may not work well or even fail. The proposal aims to develop cutting-edge statistical inference techniques and theories for a broad variety of parametric and nonparametric problems under unknown nonstationarity and dependence. The results from this project can be widely applied to data from climatic, economic, financial, and longitudinal studies. The project will integrate research and education through involvement of both undergraduate and graduate students. The investigator will disseminate research results through teaching, publications, and seminar presentations.