Consistency of the Local Kernel Density Estimator

• Main Author: Geof Givens
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 1994
• Subjects: Key Words; Kernel Density Estimate; Nonparametric; Consistency; north slope; Alaska
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.3464; http://www.stat.colostate.edu/~geof/documents/local.kernel.ps

The consistency of the local kernel density estimator is proved. This nonparametric estimator is distinguished by its use of scaling matrices which are random and which may vary for each sample point. Its applications include adaptive construction of importance sampling functions. Key Words: Kernel Density Estimate, Nonparametric, Consistency 1 Introduction If x 1 : : : x n is a random sample from a d-dimensional probability density function f(x), then a common estimate of f(x), particularly when f is continuous, is the nonparametric kernel density estimate (Rosenblatt, 1956; Parzen, 1962) f(x) = 1 nh d n n X i=1 K ` x \Gamma x i h n ' (1) Correspondence to: Geof H. Givens, Department of Statistics, Colorado State University, Fort Collins, CO 80523. This research was supported by the North Slope Borough, Alaska, the State of Alaska (through the Alaska Department of Fish and Game), and the National Oceanic and Atmospheric Administration (through the National Marine Ma.