A Test of Singularity for Distribution Functions

Posted: 1 Feb 2011

See all articles by Victoria Zinde‐Walsh

Victoria Zinde‐Walsh

McGill University - Department of Economics

John W. Galbraith

McGill University - Department of Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO)

Date Written: January 31, 2011

Abstract

Many non- and semi- parametric estimators have asymptotic properties that have been established under conditions that exclude the possibility of singular parts in the distribution. It is thus important to be able to test for absence of singularities. Methods of testing that focus on specific singularities do exist, but there are few generally applicable approaches. A general test based on kernel density estimation was proposed by Frigyesi and Hössjer (1998), but this statistic can diverge for some absolutely continuous distributions. Here we use a result in Zinde-Walsh (2008) to characterize distributions with varying degrees of smoothness, via functionals that reveal the behavior of the bias of the kernel density estimator. The statistics proposed here have well defined asymptotic distributions that are asymptotically pivotal in some class of distributions (e.g. for continuous density) and diverge for distributions in an alternative class, at a rate that can be explicitly evaluated and controlled.

Keywords: generalized function, kernel density estimator, singularity

JEL Classification: C14

Suggested Citation

Zinde-Walsh, Victoria and Galbraith, John W., A Test of Singularity for Distribution Functions (January 31, 2011). CIRANO - Scientific Publications 2011s-06, Available at SSRN: https://ssrn.com/abstract=1752207 or http://dx.doi.org/10.2139/ssrn.1752207

Victoria Zinde-Walsh

McGill University - Department of Economics ( email )

855 Sherbrooke Street West
Montreal, QC H3A 2T7
CANADA
514-398-4834 (Phone)
514-398-4938 (Fax)

John W. Galbraith (Contact Author)

McGill University - Department of Economics ( email )

855 Sherbrooke St. W
Montreal, Quebec H3A 2T7
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

2020 rue University, 25th floor
Montreal H3C 3J7, Quebec
Canada

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