## Abstract

Suppose X_{ij}, i=1, 2,..., k, j=1, 2,..., n_{i}, are random samples from independent populations distributed according to an exponential family with parameter θ_{i}. Let Y_{i} be the minimal sufficient statistic for population i and assume that the sum of any subset of the Y_{i}, 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: θ_{1}=θ_{2}= ⋯ =θ_{k} 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 language | American English |
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Pages (from-to) | 351-355 |

Number of pages | 5 |

Journal | Statistics and Probability Letters |

Volume | 12 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1991 |

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Keywords

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