A Bootstrap Test for Single Index Models

Wolfgang Haerdle, Enno Mammen and Isabel Proença (isabelp@iseg.ulisboa.pt)
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Wolfgang Haerdle: Humboldt-University of Berlin

Econometrics from University Library of Munich, Germany

Abstract: Single index models are frequently used in econometrics and biometrics. Logit and Probit models are special cases with fixed link functions. In this paper we consider a bootstrap specification test that detects nonparametric deviations of the link function. The bootstrap is used with the aim to find a more accurate distribution under the null than the normal approximation. We prove that the statistic and its bootstrapped version have the same asymptotic distribution. In a simulation study we show that the bootstrap is able to capture the negative bias and the skewness of the test statistic. It yields better approximations to the true critical values and consequently it has a more accurate level and superior power properties. We propose a modification of the HH statistic which reduces considerably the dependency of the test performance on the bandwidth choice. We show that the bootstrap of this modified statistic works as well.

Keywords: Bootstrap; kernel estimate; single index model; specification test. (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2005-08-05
New Economics Papers: this item is included in nep-ecm
Note: Type of Document - pdf; prepared on windows; pages: 28
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Citations: View citations in EconPapers (1)

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Related works:
Working Paper: A Bootstrap Test for Single Index Models (1993)
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:0508007

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