On bootstrapping L2-type statistics in density testing

Sonderforschungsbereich 373, Humboldt-Universität zu Berlin, Spandauer Straße 1, D-10178 Berlin, Germany; Department of Mathematics and Statistics, University of Cyprus, P.O. Box 537, Nicosia, Cyprus
Statistics & Probability Letters 01/2000; DOI: 10.1016/S0167-7152(00)00091-2

ABSTRACT 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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