Author

Xiaoxiao Ma

Advisor

Patil, Prakash N.

Committee Member

Woody, Jonathan R.

Committee Member

Wu, Tung-Lung

Committee Member

Sepehrifar, Mohammad

Date of Degree

8-1-2019

Document Type

Graduate Thesis - Open Access

Major

Statistics

Degree Name

Master of Science

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

In this thesis we investigate the convergence rate of gamma kernel estimators in recursive density estimation. Unlike the traditional symmetric and fixed function, the gamma kernel is a kernel function with bounded support and varying shapes. Gamma kernels have been used to address the boundary bias problem which occurs when a symmetric kernel is used to estimate a density which has support on [0, ?). The recursive density estimation is useful when an 'additional data' (on-line) comes from the population density which we want to estimate. We utilize the ideas and results from the adaptive kernel estimation to show that the L_2 convergence rate of the recursive kernel density estimators which use gamma kernels is n^(-4/5).

URI

https://hdl.handle.net/11668/14483

Comments

kernel estimation||bandwidth||convergence rate||standard kernel||boundary bias||gamma kernel||recursive estimation

Share

COinS