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On the power-divergence statistic in sparse multinomial models requiring parameter estimation

Author

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  • Tiwari, Ram C.
  • Wells, Martin T.

Abstract

It will be shown that the power-divergence family of goodness-of-fit statistics for completely specified parameters and nuisance parameter, under the sparseness assumption, have the same asymptotic normal distribution under a sequence of local alternatives. Hence, these tests have such low efficiency that they can not distinguish between the known and unknown parameters. Although it seems unlikely that the test statistics with and without estimated nuisance parameters have the same asymptotic behavior, there is a simple intuitive explanation for this phenomenon. The case in which the number of nuisance parameters tends to infinity is addressed.

Suggested Citation

  • Tiwari, Ram C. & Wells, Martin T., 1992. "On the power-divergence statistic in sparse multinomial models requiring parameter estimation," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 57-60, January.
    • Handle: RePEc:eee:stapro:v:13:y:1992:i:1:p:57-60
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