Patil, Prakash N.
Woody, Jonathan R.
Date of Degree
Graduate Thesis - Open Access
Master of Science
College of Arts and Sciences
Department of Mathematics and Statistics
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).
Ma, Xiaoxiao, "On gamma kernel function in recursive density estimation" (2019). Theses and Dissertations MSU. 3358.