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A Generalized Stepwise Procedure with Improved Power for Multiple Inequalities Testing

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Abstract

We propose a stepwise test, Step-SPA(k), for multiple inequalities testing. This test is analogous to the Step-SPA test of Hsu, Hsu, and Kuan (2010, Journal of Empirical Finance) but has asymptotic control of a generalized familywise error rate: the probability of at least k false rejections. This test is also an improvement of Step-RC(k) of Romano and Wolf (2007, Annals of Statistics) because it avoids the least favorable configuration used in Step-RC(k). We show that the proposed Step-SPA(k) is consistent, in that it can identify the violated null hypotheses with probability approaching one. It is also shown analytically and by simulations that Step-SPA(k) is more powerful than Step-RC(k) under any power notion defined in Romano and Wolf (2005, Econometrica). An empirical study on CTA fund performance is also provided to illustrate this test.

Suggested Citation

  • Yu-Chin Hsu & Chung-Ming Kuan & Meng-Feng Yen, 2013. "A Generalized Stepwise Procedure with Improved Power for Multiple Inequalities Testing," IEAS Working Paper : academic research 13-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  • Handle: RePEc:sin:wpaper:13-a001
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    Keywords

    data snooping; familiywise error rate; least favorable con guration; multiple inequalities testing; Reality Check; SPA test; stepwise test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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