Bootstrap methods for multivariate hypothesis testing

ABSTRACT

The nonparametric and parametric bootstrap methods for multivariate hypothesis testing are developed. They are used to approximate the null distribution of the test statistics proposed by Duchesne and Francq (2015), resulting in bootstrap testing procedures. In the problem of testing for the mean vector of a multivariate distribution, the asymptotic validity of the bootstrap methods is proved. The finite sample performance of the new solutions is demonstrated by means of Monte Carlo simulation studies. They indicate that for small-sample size, the bootstrap tests provide a better finite sample properties than the asymptotic tests considered by Duchesne and Francq (2015).

KEYWORDS:

• Generalized inverse
• Multivariate hypothesis testing
• Nonparametric and parametric bootstrap
• Singular normal distribution
• {2}-inverse
• Wald-type test statistic

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H15
• Secondary 62F40

Acknowledgments

The author is thankful to the referee and the editor for their constructive comments that led to a substantial improvement of the article.