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On bootstrapping L2-type statistics in density testing

✍ Scribed by Michael H. Neumann; Efstathios Paparoditis

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
139 KB
Volume
50
Category
Article
ISSN
0167-7152

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✦ Synopsis

We consider non-parametric tests for checking parametric hypotheses about the stationary density of weakly dependent observations. The test statistic is based on the L2-distance between a non-parametric and a smoothed version of a parametric estimate of the stationary density. Since this statistic behaves asymptotically as in the case of independent observations an i.i.d.-type bootstrap to determine the critical value for the test is proposed.

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Suppose that \(Y\) is distributed as multivariate normal with unknown covariance matrix and that \(N\) independent observations are available on \(Y\). An important special case of the problem studied in this paper is that of testing the null hypothesis that the mean of \(Y\) is zero against the alt