On Bootstrap Tests of Hypotheses

The size of the bootstrap test of hypotheses is studied for the normal and exponential one and two-sample problems. It is found that the size depends not only on the problem, but on the choice of test statistic and the nominal level. In some special cases, the bootstrap test is UMP, but in other cases, it can be totally useless, such as being completely randomized or rejecting the null hypothesis with probability one. More importantly, the size is usually greater than the nominal level, even in the limit as the sample size goes to infinity.

[1]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[2]  J. Hidalgo,et al.  A Parametric Bootstrap Test for Cycles , 2005 .

[3]  D. Cox.  Tests of Separate Families of Hypotheses , 1961 .

[4]  E. B. Wilson,et al.  The Distribution of Chi-Square. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Michael J Campbell,et al.  The use of bootstrap methods for analysing health-related quality of life outcomes (particularly the SF-36) , 2004, Health and quality of life outcomes.

[6]  Kullapapruk Piewthongngam Sukhdial,et al.  AIDS VERSUS THE ROTTERDAM DEMAND SYSTEM: A COX TEST WITH PARAMETRIC BOOTSTRAP , 2002 .

[7]  P. Albert,et al.  Parametric and semiparametric approaches to testing for seasonal trend in serial count data. , 2002, Biostatistics.

[8]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[9]  A Cox parametric bootstrap test of the von Liebig hypotheses , 2007 .

[10]  José M. F. Moura,et al.  A GLRT and bootstrap approach to detection in magnetic resonance force microscopy , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[11]  Bryan C. Carstens,et al.  Testing population genetic structure using parametric bootstrapping and MIGRATE-N , 2005, Genetica.

[12]  J. G. Burleigh,et al.  Covarion structure in plastid genome evolution: a new statistical test. , 2005, Molecular biology and evolution.

[13]  Andrew R Solow,et al.  Testing the Power Law Model for Discrete Size Data , 2003, The American Naturalist.