Constructing unbiased tests for homogeneity and goodness of fit

Arthur Cohen, H. B. Sackrowitz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Suppose Xij, i=1, 2,..., k, j=1, 2,..., ni, are random samples from independent populations distributed according to an exponential family with parameter θi. Let Yi be the minimal sufficient statistic for population i and assume that the sum of any subset of the Yi, i=1, 2,..., k, is also a one parameter exponential family. The normal and Poisson distributions satisfy such an assumption. The problem is to test H: θ12= ⋯ =θk vs K: not H. Unbiased tests are constructed. The construction ca so that the resulting unbiased tests are in a complete class in the continuous case and are admissible in the discrete case. The construction is also appropriate for testing a simple hypothesis concerned with multinomial probabilities against an arbitrary alternative. This latter problem arises in testing goodness of fit.

Original languageAmerican English
Pages (from-to)351-355
Number of pages5
JournalStatistics and Probability Letters
Issue number4
StatePublished - Oct 1991

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Neyman structure
  • Unbiased test
  • exponential family
  • goodness of fit
  • homogeneity


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