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INFERENCE ABOUT THE MEAN OF A POISSON DISTRIBUTION IN THE PRESENCE OF A NUISANCE PARAMETER
Author(s) -
Yip Paul
Publication year - 1988
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1988.tb00624.x
Subject(s) - nuisance parameter , nuisance , poisson distribution , inference , statistics , mathematics , econometrics , restricted maximum likelihood , maximum likelihood , statistical inference , conditional probability distribution , distribution (mathematics) , computer science , artificial intelligence , law , mathematical analysis , estimator , political science
Summary In this note we examine the problem of estimating the mean of a Poisson distribution when a nuisance parameter is present. Using a condition of Cox (1958) about ancillarity in the presence of a nuisance parameter, we justify that inference about the parameter should be carried out using the conditional distribution given the appropriate ancillary statistics. A small simulation study has been done to compare the performance of the conditional likelihood approach and the standard likelihood approach.