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Hypothesis testing based on a vector of statistics

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  • King, Maxwell L.
  • Zhang, Xibin
  • Akram, Muhammad

Abstract

This paper presents a new approach to hypothesis testing based on a vector of statistics. It involves simulating the statistics under the null hypothesis and then estimating the joint density of the statistics. This allows the p-value of the smallest acceptance region test to be estimated. We prove this p-value is a consistent estimate under some regularity conditions. The small-sample properties of the proposed procedure are investigated in the context of testing for autocorrelation, testing for normality, and testing for model misspecification through the information matrix. We find that our testing procedure has appropriate sizes and good powers.

Suggested Citation

  • King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    • Handle: RePEc:eee:econom:v:219:y:2020:i:2:p:425-455
    DOI: 10.1016/j.jeconom.2020.03.010
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    1. Lena S. Bjerkander & Jonas Dovern & Hans Manner, 2024. "Testing with Vectors of Statistics: Revisiting Combined Hypothesis Tests with an Application to Specification Testing," CESifo Working Paper Series 11027, CESifo.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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