Testing many restrictions under heteroskedasticity

Stanislav Anatolyev; Mikkel Sølvsten

doi:10.1016/j.jeconom.2023.03.011

Testing many restrictions under heteroskedasticity

^*Corresponding author for this work

Department of Economics and Business Economics

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Abstract

We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.

Original language	English
Article number	105473
Journal	Journal of Econometrics
Volume	236
Issue	1
Number of pages	19
ISSN	0304-4076
DOIs	https://doi.org/10.1016/j.jeconom.2023.03.011
Publication status	Published - Sept 2023

Keywords

High-dimensional models
Hypothesis testing
Leave-out estimation
Linear regression
Many regressors
Ordinary least squares

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10.1016/j.jeconom.2023.03.011

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title = "Testing many restrictions under heteroskedasticity",

abstract = "We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.",

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T1 - Testing many restrictions under heteroskedasticity

AU - Anatolyev, Stanislav

AU - Sølvsten, Mikkel

PY - 2023/9

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N2 - We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.

AB - We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.

KW - High-dimensional models

KW - Hypothesis testing

KW - Leave-out estimation

KW - Linear regression

KW - Many regressors

KW - Ordinary least squares

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DO - 10.1016/j.jeconom.2023.03.011

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VL - 236

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 1

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ER -

Testing many restrictions under heteroskedasticity

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Keywords

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