JSM 2004 - Toronto

Abstract #300468

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Activity Number: 408
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #300468
Title: Tests for Location-scale Families Based on the Empirical Characteristic Function
Author(s): Thomas W. Epps*+
Companies: University of Virginia
Address: Economics Dept., Rouss Hall, Charlottesville, VA, 22903,
Keywords: Anderson-Darling test ; goodness-of-fit test ; BHEP test
Abstract:

A unified procedure is proposed for testing the fit of location-scale families. The principle is analogous to that of Anderson-Darling (AD) but applies the empirical characteristic function (CF) rather than the empirical distribution function (DF). Whereas AD statistics are derived as weighted integrals of squared distances between DFs of standardized data and models, the proposed CF statistics are weighted integrals of squared distances between empirical and model CFs. As do AD statistics, these have simple closed forms when squared moduli of model CFs are used as weight functions. While applications of the principle to normal and Cauchy laws are already well established, the paper extends the procedure to other location-scale models: uniform, exponential, Laplace, logistic, and extreme-value. Small-sample powers compare favorably with those of A-D and have particular advantage for uniform, exponential, Cauchy, and Laplace models.

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