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Probability estimation via smoothing in sparse contingency tables with ordered categories

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  • Simonoff, Jeffrey S.

Abstract

Probability estimation in sparse two-dimensional contingency tables with ordered categories is examined. Several smoothing procedures are compared to analysis of the unsmoothed table. It is shown that probability estimates obtained via maximum penalized likelihood smoothing are consistent under a sparse asymptotic framework if the underlying probability matrix is smooth, and are more accurate than kernel-based and other smoothing techniques. In fact, computer simulations indicate that smoothing based on a product kernel is less effective than no smoothing at all. An example is given to illustrate the smoothing technique. Possible extensions to model building and higher dimensional tables are discussed.

Suggested Citation

  • Simonoff, Jeffrey S., 1987. "Probability estimation via smoothing in sparse contingency tables with ordered categories," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 55-63, January.
    • Handle: RePEc:eee:stapro:v:5:y:1987:i:1:p:55-63
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    Citations

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    Cited by:

    1. Burman, Prabir, 2004. "On some testing problems for sparse contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 1-18, January.
    2. Granville, Vincent, 1996. "Discriminant analysis and density estimation on the finite d-dimensional grid," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 27-51, June.
    3. Bartolucci, F. & Scaccia, L., 2004. "Testing for positive association in contingency tables with fixed margins," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 195-210, August.
    4. Ivy Liu & Alan Agresti, 2005. "The analysis of ordered categorical data: An overview and a survey of recent developments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-73, June.
    5. Faisal Maqbool Zahid & Gerhard Tutz, 2013. "Proportional Odds Models with High‐Dimensional Data Structure," International Statistical Review, International Statistical Institute, vol. 81(3), pages 388-406, December.

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