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An omnibus test of goodness-of-fit for conditional distributions with applications to regression models

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Title: An omnibus test of goodness-of-fit for conditional distributions with applications to regression models
Authors: Ducharme, Gilles R.1 gilles.ducharme@univ-montp2.fr, Ferrigno, Sandie2 sandie.ferrigno@iecn-unancy.fr
Source: Journal of Statistical Planning & Inference. Oct2012, Vol. 142 Issue 10, p2748-2761. 14p.
Subjects: Goodness-of-fit tests, Distribution (Probability theory), Regression analysis, Random variables, Polynomials, Parameter estimation, Simulation methods & models, Nonparametric statistics
Abstract: Abstract: We introduce an omnibus goodness-of-fit test for statistical models for the conditional distribution of a random variable. In particular, this test is useful for assessing whether a regression model fits a data set on all its assumptions. The test is based on a generalization of the Cramér–von Mises statistic and involves a local polynomial estimator of the conditional distribution function. First, the uniform almost sure consistency of this estimator is established. Then, the asymptotic distribution of the test statistic is derived under the null hypothesis and under contiguous alternatives. The extension to the case where unknown parameters appear in the model is developed. A simulation study shows that the test has good power against some common departures encountered in regression models. Moreover, its power is comparable to that of other nonparametric tests designed to examine only specific departures. [Copyright &y& Elsevier]
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Database: Engineering Source
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Abstract:Abstract: We introduce an omnibus goodness-of-fit test for statistical models for the conditional distribution of a random variable. In particular, this test is useful for assessing whether a regression model fits a data set on all its assumptions. The test is based on a generalization of the Cramér–von Mises statistic and involves a local polynomial estimator of the conditional distribution function. First, the uniform almost sure consistency of this estimator is established. Then, the asymptotic distribution of the test statistic is derived under the null hypothesis and under contiguous alternatives. The extension to the case where unknown parameters appear in the model is developed. A simulation study shows that the test has good power against some common departures encountered in regression models. Moreover, its power is comparable to that of other nonparametric tests designed to examine only specific departures. [Copyright &y& Elsevier]
ISSN:03783758
DOI:10.1016/j.jspi.2012.04.008