IPLS Seminar: Dr Yunyi Zhang (The Chinese University of Hong Kong, Shenzhen)

Abstract: Classical statistical inference methodologies were originally developed under the assumption of data independence. However, the independent assumption has become excessively restrictive in various scenarios, especially when the data are collected in a sequential manner, such as having time labels. If the independent assumption cannot be ensured, then the observed data may exhibit strong correlations, which leads to erroneous inferences.

The time series literature was later introduced to address those dependency and correlations. However, to validate results in the literature, statisticians of- ten resort to introducing sorts of stationary assumptions. These assumptions entail either the covariances of the data only depend on the lag between data rather than the time labels, or the joint distributions of the data being identi- cal. Unfortunately, these stationary assumptions are too stringent for real–life datasets to satisfy, and is hard to verify through hypothesis testing. This pre- sentation aims to introduce statistical inference methodologies to deal with the potential non–stationarity in dependent data.

This presentation primarily concerns high–dimensional linear regression and univariate autoregression. For the linear regression yi = Xiβ + εi with time– series dependent (correlated) and heterogeneous errors εi, we explore the testing of linear combinations of coefficients Aβ = c . In the autoregressive model, we consider generating the simultaneous confidence intervals for the autoregressive coefficients within the model Xi = Ppj=1 aj Xi−j + εi with white noise but not necessarily independent errors εi.

To streamline calculations, we introduce the dependent wild bootstrap, a computer–intensive method designed to assist statisticians in generating confi- dence intervals and conducting hypothesis testing through simulations. Numer- ical simulations reveals distinctions between our work and the common methods when observations fail to meet independent or stationary assumptions. For as- suming observations as independent or stationary can be unrealistic in practical scenarios, our approach provides a good alternative in such cases.

Host: Wenying Shou