Hypothesis testing in a generic nesting framework for general distributions Articles uri icon

authors

  • MARTIN APAOLAZA, NIRIAN
  • BALAKRISHNAN, N.

publication date

  • July 2013

start page

  • 1

end page

  • 23

volume

  • 118

international standard serial number (ISSN)

  • 0047-259X

electronic international standard serial number (EISSN)

  • 1095-7243

abstract

  • Nested parameter spaces, either in the null or alternative hypothesis, often enable an improvement in the performance of the tests. In this context, order restricted inference has not been studied in detail. Divergence based measures provide a flexible tool for proposing some useful test statistics, which usually contain the likelihood ratio-test statistics as a special case. The existing literature on hypothesis testing under inequality constraints, based on phi-divergence measures, is concentrated on specific models with multinomial sampling. In this paper the existing results are extended and unified through new families of test-statistics that are valid for nested parameter spaces containing either equality or inequality constraints and general distributions for either single or multiple populations.

keywords

  • chi-bar-square statistic; chi-square statistic; divergence based test statistics; equality constraints; exponential family of distributions; inequality constraints