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October, 1995 Consistency and Monte Carlo Simulation of a Data Driven Version of Smooth Goodness-of-Fit Tests
Wilbert C. M. Kallenberg, Teresa Ledwina
Ann. Statist. 23(5): 1594-1608 (October, 1995). DOI: 10.1214/aos/1176324315


The data driven method of selecting the number of components in Neyman's smooth test for uniformity, introduced by Ledwina, is extended. The resulting tests consist of a combination of Schwarz's Bayesian information criterion (BIC) procedure and smooth tests. The upper bound of the dimension of the exponential families in applying Schwarz's rule is allowed to grow with the number of observations to infinity. Simulation results show that the data driven version of Neyman's test performs very well for a wide range of alternatives and is competitive with other recently introduced (data driven) procedures. It is shown that the data driven smooth tests are consistent against essentially all alternatives. In proving consistency, new results on Schwarz's selection rule are derived, which may be of independent interest.


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Wilbert C. M. Kallenberg. Teresa Ledwina. "Consistency and Monte Carlo Simulation of a Data Driven Version of Smooth Goodness-of-Fit Tests." Ann. Statist. 23 (5) 1594 - 1608, October, 1995.


Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0847.62035
MathSciNet: MR1370299
Digital Object Identifier: 10.1214/aos/1176324315

Primary: 62G10
Secondary: 62E25 , 62G20

Keywords: exponential family , Goodness-of-fit , Monte Carlo power , Neyman's test , Schwarz's BIC criterion , smooth test

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 5 • October, 1995
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