The Annals of Statistics

Data driven smooth tests for composite hypotheses

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

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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

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

First available in Project Euclid: 20 November 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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