Test for model selection using Cramér–von Mises distance in a fixed design regression setting

Hong Chen, Maik Döring () and Uwe Jensen
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Hong Chen: University of Hohenheim
Maik Döring: University of Hohenheim
Uwe Jensen: University of Hohenheim

AStA Advances in Statistical Analysis, 2018, vol. 102, issue 4, No 2, 505-535

Abstract: Abstract In this paper a test for model selection is proposed which extends the usual goodness-of-fit test in several ways. It is assumed that the underlying distribution H depends on a covariate value in a fixed design setting. Secondly, instead of one parametric class we consider two competing classes one of which may contain the underlying distribution. The test allows to select one of two equally treated model classes which fits the underlying distribution better. To define the distance of distributions various measures are available. Here the Cramér-von Mises has been chosen. The null hypothesis that both parametric classes have the same distance to the underlying distribution H can be checked by means of a test statistic, the asymptotic properties of which are shown under a set of suitable conditions. The performance of the test is demonstrated by Monte Carlo simulations. Finally, the procedure is applied to a data set from an endurance test on electric motors.

Keywords: Test for model selection; Goodness-of-fit; Fixed design regression; Cramér–von Mises distance (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10182-017-0317-0

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