Local rank tests in a multivariate nonparametric relationship

Natércia Fortuna

FEP Working Papers from Universidade do Porto, Faculdade de Economia 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.

Keywords: nonparametric relationship; local rank; local rank estimation; kernel smoothing; consistent tests; demand systems. (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 D12 (search for similar items in EconPapers)
Pages: 46 pages
Date: 2004-02
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Local rank tests in a multivariate nonparametric relationship (2008)
Working Paper: Local rank tests in a multivariate nonparametric relationship (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:por:fepwps:137

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