A new test for the parametric form of the variance function in non-parametric regression
In the common non-parametric regression model the problem of testing for the parametric form of the conditional variance is considered. A stochastic process based on the difference between the empirical processes that are obtained from the standardized non-parametric residuals under the null hypothesis (of a specific parametric form of the variance function) and the alternative is introduced and its weak convergence established. This result is used for the construction of a Kolmogorov-Smirnov and a Cramér-von Mises type of statistic for testing the parametric form of the conditional variance. The consistency of a bootstrap approximation is established, and the finite sample properties of this approximation are investigated by means of a simulation study. In particular the new procedure is compared with some of the currently available methods for this problem. Copyright 2007 Royal Statistical Society.
Year of publication: |
2007
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Authors: | Dette, Holger ; Neumeyer, Natalie ; Keilegom, Ingrid Van |
Published in: |
Journal of the Royal Statistical Society Series B. - Royal Statistical Society - RSS, ISSN 1369-7412. - Vol. 69.2007, 5, p. 903-917
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Publisher: |
Royal Statistical Society - RSS |
Saved in:
freely available
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