The Annals of Statistics

Asymptotic Comparison of Cramer-von Mises and Nonparametric Function Estimation Techniques for Testing Goodness-of-Fit

R. L. Eubank and V. N. LaRiccia

Full-text: Open access

Abstract

Two new statistics for testing goodness-of-fit are derived from the viewpoint of nonparametric density estimation. These statistics are closely related to the Neyman smooth and Cramer-von Mises statistics but are shown to have superior properties both through asymptotic and small sample analyses. Comparison of the proposed tests with the Cramer-von Mises statistic requires the development of a novel technique for comparing tests that are capable of detecting local alternatives converging to the null at different rates.

Article information

Source
Ann. Statist., Volume 20, Number 4 (1992), 2071-2086.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348903

Digital Object Identifier
doi:10.1214/aos/1176348903

Mathematical Reviews number (MathSciNet)
MR1193326

Zentralblatt MATH identifier
0769.62033

JSTOR
links.jstor.org

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62E20: Asymptotic distribution theory

Keywords
Asymptotic efficiency density estimation Fourier series high frequency alternatives

Citation

Eubank, R. L.; LaRiccia, V. N. Asymptotic Comparison of Cramer-von Mises and Nonparametric Function Estimation Techniques for Testing Goodness-of-Fit. Ann. Statist. 20 (1992), no. 4, 2071--2086. doi:10.1214/aos/1176348903. https://projecteuclid.org/euclid.aos/1176348903


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