Local rank tests in a multivariate nonparametric relationship

• Type: Article in International Scientific Journal
• Date: 2008

Authors

Natércia Fortuna (Author) FEP

Journal

Title: Journal of Econometrics

Vol. 142 No. 1

Pages: 162-182

ISSN: 0304-4076

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 2 Citations

ISI Web of Science

Scopus - 2 Citations

Scientific classification

FOS: Social sciences

CORDIS: Social sciences

Other information

Authenticus ID: P-004-3V9

DOI: 10.1016/j.jeconom.2007.03.001

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21