Statistics Seminar: Wen Zhou, Colorado State University
Estimation and Inference of a Heteroskedasticity Model with Latent Semiparametric Factors for Panel Data Analysis
We consider estimation and inference of a flexible subject-specific heteroskedasticity model for analyzing large scale panel data, which employs latent semiparametric factor structure to simultaneously account for the heteroskedasticity across subjects and contemporaneous correlations. Specifically, the heteroskedasticity across subjects is modeled by the product of unobserved stationary process of factors and subject-specific covariate effect. Serving as the loading, the covariate effect is further modeled through the additive model. We propose a two-step procedure for estimation. First, the latent factor process and nonparametric loading are estimated via projection-based methods. The estimation of regression coefficients is further conducted through the generalized least squares type approach. Theoretical validity of the two-step procedure is carefully documented. By scrupulously examining the non-asymptotic rates for recovering the latent factor process and its loading, we further study the properties of the estimated regression coefficients. In particular, we establish the asymptotic normality of the proposed two-step estimate of regression coefficients. The proposed regression coefficient estimator is also shown to be asymptotically efficient. This leads to a more efficient confidence set of the regression coefficients. Using a comprehensive simulation study, we demonstrate the finite sample performance of the proposed procedure, and numerical results corroborate our theoretical findings. Finally, we apply our proposed method to a data set of air quality and energy consumption collected at 129 monitoring sites in the United States in 2015. This is a collaborative work with Lvuou Zhang and Haonan Wang.
Refreshments will be served at 3:00pm in the 3rd floor lounge of Hanes Hall