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Robust hypothesis tests for M‐estimators with possibly non‐differentiable estimating functions

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  • Wei‐Ming Lee
  • Yu‐Chin Hsu
  • Chung‐Ming Kuan

Abstract

We propose a new robust hypothesis test for (possibly non‐linear) constraints on M‐estimators with possibly non‐differentiable estimating functions. The proposed test employs a random normalizing matrix computed from recursive M‐estimators to eliminate the nuisance parameters arising from the asymptotic covariance matrix. It does not require consistent estimation of any nuisance parameters, in contrast with the conventional heteroscedasticity‐autocorrelation consistent (HAC)‐type test and the Kiefer–Vogelsang–Bunzel (KVB)‐type test. Our test reduces to the KVB‐type test in simple location models with ordinary least‐squares estimation, so the error in the rejection probability of our test in a Gaussian location model is O p ( T − 1 log T ) . We discuss robust testing in quantile regression, and censored regression models in detail. In simulation studies, we find that our test has better size control and better finite sample power than the HAC‐type and KVB‐type tests.

Suggested Citation

  • Wei‐Ming Lee & Yu‐Chin Hsu & Chung‐Ming Kuan, 2015. "Robust hypothesis tests for M‐estimators with possibly non‐differentiable estimating functions," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 95-116, February.
  • Handle: RePEc:wly:emjrnl:v:18:y:2015:i:1:p:95-116
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    File URL: http://hdl.handle.net/10.1111/ectj.12041
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    Cited by:

    1. Lee, Wei-Ming & Kuan, Chung-Ming & Hsu, Yu-Chin, 2014. "Testing over-identifying restrictions without consistent estimation of the asymptotic covariance matrix," Journal of Econometrics, Elsevier, vol. 181(2), pages 181-193.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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