Asymptotic properties of a two sample randomized test for partially dependent data

Grzegorz A. Rempala, Stephen Warwick Looney

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We are concerned with an issue of asymptotic validity of a non-parametric randomization test for the two sample location problem under the assumption of partially dependent observations, in which case the validity of the usual permutation t-test breaks down. We show that a certain modification of the permutation group used in the randomization procedure yields an unconditional asymptotically valid test in the sense that its probability of Type I error tends to the nominal level with increasing sample sizes. We show that this unconditional test is equivalent to the one based on a linear combination of two- and one-sample t-statistics and enjoys some optimal power properties. We also conduct a simulation study comparing our approach with that based on the Fisher's method of combining p-values. Finally, we present an example of application of the test in a medical study on functional status assessment at the end of life.

Original languageEnglish (US)
Pages (from-to)68-89
Number of pages22
JournalJournal of Statistical Planning and Inference
Volume136
Issue number1
DOIs
StatePublished - Jan 1 2006

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Functional assessment
Dependent Data
Asymptotic Properties
Unconditional Test
Statistics
Randomization Test
Dependent Observations
Two-sample Problem
Permutation Test
Type I error
t-test
Non-parametric test
Permutation group
Location Problem
p-Value
Randomisation
Categorical or nominal
Breakdown
Linear Combination
Sample Size

Keywords

  • Consistency
  • Hypothesis test
  • Randomization test
  • Relative efficiency
  • Two sample problem

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Asymptotic properties of a two sample randomized test for partially dependent data. / Rempala, Grzegorz A.; Looney, Stephen Warwick.

In: Journal of Statistical Planning and Inference, Vol. 136, No. 1, 01.01.2006, p. 68-89.

Research output: Contribution to journalArticle

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