Selecting the Smoothing Parameter in Goodness of Fit Testing
Abstract
Once again the use of nonparametric density estimators to test
goodness of fit (GOF) hypotheses have become popular. A major
difficulty with such approaches is determining how the smoothing
parameter should be selected. These problems are illustrated by
considering the test procedure, for a simple null hypothesis, based on
the
L-1 difference between the histogram estimator and its expected value,
under the null hypothesis. The power of this test is a function of D
(the L-1 distance between the expected value of the histogram and its
expected value under the null), n (the sample size) and M (The number
of cells in the histogram). For each value of M, n and D the power
envelope of this test is determined. This is done by determining the
two pdfs which maximize and minimize the power of the test. Let P(m,
M, D) denote the minimum power of the test for fixed values of n, M,
and D. The value of M required for P(m, M, D) to satisfy different
asymptotic criteria are also determined. Surprisingly the values
required vary dramatically, from M=2 for all values of n to M
approximately equal to n.
R E F R E S H M E N T S
4:00 To 4:25 PM
Kenneth W. Anderson
Memorial Reading Room
