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Local rank tests in a multivariate nonparametric relationship

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  • Natércia Fortuna

    (CEMPRE, Faculdade de Economia da Universidade do Porto)

Abstract

Consider a multivariate nonparametric model where the unknown vector of functions depends on two sets of explanatory variables. For a fixed level of one set of explanatory variables, we provide consistent statistical tests, called local rank tests, to determine whether the multivariate relationship can be explained by a smaller number of functions. We also provide estimators for the smallest number of functions, called local rank, explaining the relationship. The local rank tests and the estimators of local rank are defined in terms of the eigenvalues of a kernel-based estimator of some matrix. The asymptotics of the eigenvalues is established by using the so-called Fujikoshi expansion along with some techniques of the theory of U-statistics. We present a simulation study which examines the small sample properties of local rank tests. We also apply the local rank tests and the local rank estimators to a demand system given by a newly constructed data set. This work can be viewed as a “local” extension of the tests for a number of factors in a nonparametric relationship introduced by Stephen Donald.

Suggested Citation

  • Natércia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," FEP Working Papers 137, Universidade do Porto, Faculdade de Economia do Porto.
  • Handle: RePEc:por:fepwps:137
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    References listed on IDEAS

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    1. Lewbel, Arthur, 1989. "A Demand System Rank Theorem," Econometrica, Econometric Society, vol. 57(3), pages 701-705, May.
    2. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
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    8. Christopher J. Nicol, 2001. "The rank and model specification of demand systems: an empirical analysis using United States microdata," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 34(1), pages 259-289, February.
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    1. Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.
    2. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2011. "Local and Global Rank Tests for Multivariate Varying-Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 295-306.
    3. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1217-1232, December.

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    More about this item

    Keywords

    nonparametric relationship; local rank; local rank estimation; kernel smoothing; consistent tests; demand systems.;
    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
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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