Gradient statistic: higher-order asymptotics and Bartlett-type correction

2012/06/11 by Tiago M. Vargas, Vargas, Tiago M., Silvia L. P. Ferrari +3
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1206.2206

Submitted for publication

arxiv created 2012/06/11 · openalex publication_date 2012/06/11 · arxiv updated 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an asymptotic expansion for the null distribution function of thegradient 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 Ghosh and Mukerjee (1991). 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. A small Monte Carlo experiment and various examples are presented and discussed.

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