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A general theory of rank testing

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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, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2015.
  • Handle: RePEc:upf:upfgen:1411
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    Cited by:

    1. Majid M. Al-Sadoon, 2015. "Testing subspace Granger causality," Economics Working Papers 1495, Department of Economics and Business, Universitat Pompeu Fabra.
    2. repec:eee:econom:v:199:y:2017:i:1:p:49-62 is not listed on IDEAS
    3. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers CWP60/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    Rank testing; cointegration; plug-in principle; subspace estimation.;

    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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