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June 1997 Data driven smooth tests for composite hypotheses
Tadeusz Inglot, Wilbert C. M. Kallenberg, Teresa Ledwina
Ann. Statist. 25(3): 1222-1250 (June 1997). DOI: 10.1214/aos/1069362746


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.


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Tadeusz Inglot. Wilbert C. M. Kallenberg. Teresa Ledwina. "Data driven smooth tests for composite hypotheses." Ann. Statist. 25 (3) 1222 - 1250, June 1997.


Published: June 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0904.62055
MathSciNet: MR1447749
Digital Object Identifier: 10.1214/aos/1069362746

Primary: 62G10 , 62G20

Keywords: data driven procedure , Goodness-of-fit , Neyman's test , Schwarz's BIC criterion , smooth test

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 3 • June 1997
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