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2013 Gradient statistic: Higher-order asymptotics and Bartlett-type correction
Tiago M. Vargas, Silvia L.P. Ferrari, Artur J. Lemonte
Electron. J. Statist. 7: 43-61 (2013). DOI: 10.1214/12-EJS763


We obtain an asymptotic expansion for the null distribution function of the gradient statistic for testing composite null hypotheses in the presence of nuisance parameters. The expansion is derived using a Bayesian route based on the shrinkage argument described in [10]. Using this expansion, we propose a Bartlett-type corrected gradient statistic with chi-square distribution up to an error of order $o(n^{-1})$ under the null hypothesis. Further, we also use the expansion to modify the percentage points of the large sample reference chi-square distribution. Monte Carlo simulation experiments and various examples are presented and discussed.


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Tiago M. Vargas. Silvia L.P. Ferrari. Artur J. Lemonte. "Gradient statistic: Higher-order asymptotics and Bartlett-type correction." Electron. J. Statist. 7 43 - 61, 2013.


Published: 2013
First available in Project Euclid: 11 January 2013

zbMATH: 1336.62143
MathSciNet: MR3020413
Digital Object Identifier: 10.1214/12-EJS763

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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