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L2-tests for sparse multinomials

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  • Liero, Hannelore

Abstract

We consider the problem of testing cell probabilities in sparse multinomial data sets. The first test statistic is the sum of squares of differences between the hypothetical cell probabilities and the relative cell frequencies. For the second test we use the differences between smoothed hypothetical cell probabilities and smoothed cell frequencies. A comparison of both tests with respect to the behavior of their power under local alternatives shows that for sparse data the test based on the smoothed estimators is better.

Suggested Citation

  • Liero, Hannelore, 2001. "L2-tests for sparse multinomials," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 147-158, November.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:2:p:147-158
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    References listed on IDEAS

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    1. Burman, Prabir, 1987. "Central limit theorem for quadratic forms for sparse tables," Journal of Multivariate Analysis, Elsevier, vol. 22(2), pages 258-277, August.
    2. Konakov, V. & Läuter, H. & Liero, H., 1995. "Nonparametric versus Parametric Goodness of Fit," SFB 373 Discussion Papers 1995,49, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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