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On the asymptotic behaviour of the integrated square error of kernel density estimators with data-dependent bandwidth

โœ Scribed by Carlos Tenreiro

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
131 KB
Volume
53
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

In this paper, we consider the integrated square error Jn = { f n (x) -f(x)} 2 d x; where f is the common density function of the independent and identically distributed random vectors X1; : : : ; Xn and f n is the kernel estimator with a data-dependent bandwidth. Using the approach introduced by Hall (J. Multivariate Anal. 14 (1984) 1), and under some regularity conditions, we derive the L2 consistency in probability of f n and we establish an asymptotic expansion in probability and a central limit theorem for Jn.

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