Applied and Computational Mathematics Seminar

Title: Bandwidth selection for single-index models and its application in a von-Neuman-type goodness-of-fit test

Speaker: Wei Lin, Department of Mathematics, Ohio University

Abstract: Single-index models (SIMs) are appealing mainly due to the ability in dimension reduction. Since the SIM is a natural extension to the classical linear models, it is very important to practitioners who mainly use linear models in their fields as statistical analysis tools to be able to tell whether a SIM is truly more appropriate for their data than a regular linear model. Moreover, the bandwidth selection problem for the kernel estimation of the regression function has been addressed only under very restricted conditions that can hardly be satisfied in practice.
   In this talk, I will provide a proof for the asymptotic normality of the least square estimator for the index vector in a SIM, using a practically meaningful data-driven bandwidth selection method, assuming conditions much weaker than those existing in the literature. And I will introduce a simple goodness-of-fit test for linear models versus SIMs. The asymptotic normality of the TS will be established. For empirical study, the Wild Bootstrap method has been widely used in finding the critical values, especially for hypotheses testing procedures concerning regression models. I will briefly introduce the Wild Bootstrap and other bootstrap methods. The simulation results using both asymptotic critical values and bootstrapped critical values will be prsented to show the finite sample performance of the proposed test.