The Annals of Statistics

Data driven smooth tests for composite hypotheses

Tadeusz Inglot, Wilbert C. M. Kallenberg, and Teresa Ledwina

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Abstract

The classical problem of testing goodness-of-fit of a parametric family is reconsidered. A new test for this problem is proposed and investigated. The new test statistic is a combination of the smooth test statistic and Schwarz's selection rule. More precisely, as the sample size increases, an increasing family of exponential models describing departures from the null model is introduced and Schwarz's selection rule is presented to select among them. Schwarz's rule provides the "right" dimension given by the data, while the smooth test in the "right" dimension finishes the job. Theoretical properties of the selection rules are derived under null and alternative hypotheses. They imply consistency of data driven smooth tests for composite hypotheses at essentially any alternative.

Article information

Source
Ann. Statist., Volume 25, Number 3 (1997), 1222-1250.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362746

Digital Object Identifier
doi:10.1214/aos/1069362746

Mathematical Reviews number (MathSciNet)
MR1447749

Zentralblatt MATH identifier
0904.62055

Subjects
Primary: 62G20: Asymptotic properties 62G10: Hypothesis testing

Keywords
Schwarz's BIC criterion data driven procedure goodness-of-fit smooth test Neyman's test

Citation

Inglot, Tadeusz; Kallenberg, Wilbert C. M.; Ledwina, Teresa. Data driven smooth tests for composite hypotheses. Ann. Statist. 25 (1997), no. 3, 1222--1250. doi:10.1214/aos/1069362746. https://projecteuclid.org/euclid.aos/1069362746


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