Bootstrap critical values for tests based on the smoothed maximum score estimator

Joel L. Horowitz

doi:10.1016/S0304-4076(02)00102-1

Bootstrap critical values for tests based on the smoothed maximum score estimator

Joel L. Horowitz^*

^*Corresponding author for this work

Economics

Research output: Contribution to journal › Conference article › peer-review

27 Scopus citations

Abstract

The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions. However, the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first-order asymptotics are used to obtain critical values. This paper gives conditions under which the differences between the true and nominal levels can be reduced by using the bootstrap to obtain critical values. A set of Monte Carlo experiments illustrates the numerical performance of the bootstrap.

Original language	English (US)
Pages (from-to)	141-167
Number of pages	27
Journal	Journal of Econometrics
Volume	111
Issue number	2
DOIs	https://doi.org/10.1016/S0304-4076(02)00102-1
State	Published - Dec 2002
Event	Finite Sample and Asymptotic Methods in Econometrics - Amsterdam, Netherlands Duration: Dec 11 1997 → Dec 11 1997

Keywords

Asymptotic refinement
Binary response
Edgeworth expansion
Hypothesis test

ASJC Scopus subject areas

Economics and Econometrics

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10.1016/S0304-4076(02)00102-1

Cite this

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title = "Bootstrap critical values for tests based on the smoothed maximum score estimator",

abstract = "The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions. However, the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first-order asymptotics are used to obtain critical values. This paper gives conditions under which the differences between the true and nominal levels can be reduced by using the bootstrap to obtain critical values. A set of Monte Carlo experiments illustrates the numerical performance of the bootstrap.",

keywords = "Asymptotic refinement, Binary response, Edgeworth expansion, Hypothesis test",

author = "Horowitz, {Joel L.}",

note = "Funding Information: Research supported in part by NSF grants SBR-9307677 and SBR-9617925. Part of the research was carried out while I was visiting the Institute of Statistics and Econometrics, Humboldt University, Berlin, with support from Deutsche Forschungsgemeinschaft Sonderforschungsbereich 373, “Quantifikation und Simulation {\"O}konomischer Prozesse.” I thank Oliver Linton and Gene Savin for comments on an earlier draft of this paper.; Finite Sample and Asymptotic Methods in Econometrics ; Conference date: 11-12-1997 Through 11-12-1997",

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N1 - Funding Information: Research supported in part by NSF grants SBR-9307677 and SBR-9617925. Part of the research was carried out while I was visiting the Institute of Statistics and Econometrics, Humboldt University, Berlin, with support from Deutsche Forschungsgemeinschaft Sonderforschungsbereich 373, “Quantifikation und Simulation Ökonomischer Prozesse.” I thank Oliver Linton and Gene Savin for comments on an earlier draft of this paper.

PY - 2002/12

Y1 - 2002/12

N2 - The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions. However, the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first-order asymptotics are used to obtain critical values. This paper gives conditions under which the differences between the true and nominal levels can be reduced by using the bootstrap to obtain critical values. A set of Monte Carlo experiments illustrates the numerical performance of the bootstrap.

AB - The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions. However, the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first-order asymptotics are used to obtain critical values. This paper gives conditions under which the differences between the true and nominal levels can be reduced by using the bootstrap to obtain critical values. A set of Monte Carlo experiments illustrates the numerical performance of the bootstrap.

KW - Asymptotic refinement

KW - Binary response

KW - Edgeworth expansion

KW - Hypothesis test

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DO - 10.1016/S0304-4076(02)00102-1

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VL - 111

SP - 141

EP - 167

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

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T2 - Finite Sample and Asymptotic Methods in Econometrics

Y2 - 11 December 1997 through 11 December 1997

ER -

Bootstrap critical values for tests based on the smoothed maximum score estimator

Abstract

Keywords

ASJC Scopus subject areas

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