On a weighted bootstrap approximation of the Lp norms of kernel density estimators

by Bo Liu

Institution: California State University – Northridge
Year: 2015
Keywords: Density; Dissertations, Academic  – CSUN  – Mathematics.
Posted: 02/05/2017
Record ID: 2135472
Full text PDF: http://hdl.handle.net/10211.3/145014


A weighted bootstrap method is considered to approximate the distribution of the Lp norms of kernel density estimates. Here p>=1. Using a Komlos-Major-Tusnady type approximation (Komlos et al., 1975) for the weighted bootstrap processes by a sequence of Brownian bridges, due to Horvath et al. (2000), we establish an unconditional bootstrap Central Limit Theorems (CLT) for these Lp statistics. Furthermore, through simulation studies, it will be shown that, depending on the weights chosen, the proposed approximation can outperform both the classical large-sample theory as well as Efron???s (1979) original bootstrap algorithm. Advisors/Committee Members: Mojirsheibani, Majid (advisor), Watkins, Ann E (committee member).