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A General Theory of Rank Testing

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  • Majid M. Al-Sadoon

Abstract

This paper demonstrates that all rank test statistics are functions of implicit null space estimators. The paper proposes a novel theory of null space estimation that allows for standard asymptotics, polynomial regressions, and cointegration asymptotics. The paper proves that the behaviour of rank test statistics is completely governed by the implicit null space estimators through a plug-in principle. This allows for a general theory of rank testing that simplifies the asymptotics of rank test statistics, clarifies the relationships between the various rank test statistics, makes full use of the numerical analysis literature, and motivates numerous new rank test statistics. A brief Monte Carlo study illustrates the results.

Suggested Citation

  • Majid M. Al-Sadoon, 2015. "A General Theory of Rank Testing," Working Papers 750, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:750
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    References listed on IDEAS

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    Cited by:

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    3. Al-Sadoon, Majid M., 2019. "Testing subspace Granger causality," Econometrics and Statistics, Elsevier, vol. 9(C), pages 42-61.

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    More about this item

    Keywords

    rank testing; cointegration; plug-in principle; subspace estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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