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M‐estimation Under a Two‐Sample Semiparametric Model

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  • Biao Zhang

Abstract

We consider M‐estimation under a two‐sample semiparametric model in which the log ratio of two unknown density functions has a known parametric form. This two‐sample semiparametric model, arising naturally from case‐control studies and logistic discriminant analysis, can be regarded as a biased sampling model. A new class of M‐estimators are constructed on the basis of the maximum semiparametric likelihood estimator of the underlying distribution function. It is shown that the proposed M‐estimators are consistent and asymptotically normally distributed. A simulation study is presented to demonstrate the performance of the proposed M‐estimators.

Suggested Citation

  • Biao Zhang, 2000. "M‐estimation Under a Two‐Sample Semiparametric Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 263-280, June.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:2:p:263-280
    DOI: 10.1111/1467-9469.00188
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    Cited by:

    1. José Cristóbal & José Alcalá, 2001. "An overview of nonparametric contributions to the problem of functional estimation from biased data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 309-332, December.
    2. Zhang, Biao, 2006. "Prospective and retrospective analyses under logistic regression models," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 211-230, January.

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