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Mean‐Based Iterative Procedures in Linear Models with General Errors and Grouped Data

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  • Carlos Rivero
  • Teófilo Valdés

Abstract

. We present in this paper iterative estimation procedures, using conditional expectations, to fit linear models when the distributions of the errors are general and the dependent data stem from a finite number of sources, either grouped or non‐grouped with different classification criteria. We propose an initial procedure that is inspired by the expectation‐maximization (EM) algorithm, although it does not agree with it. The proposed procedure avoids the nested iteration, which implicitly appears in the initial procedure and also in the EM algorithm. The stochastic asymptotic properties of the corresponding estimators are analysed.

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  • Carlos Rivero & Teófilo Valdés, 2004. "Mean‐Based Iterative Procedures in Linear Models with General Errors and Grouped Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 469-486, September.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:3:p:469-486
    DOI: 10.1111/j.1467-9469.2004.01_108.x
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    Cited by:

    1. Peter Bickel & Bo Li & Alexandre Tsybakov & Sara Geer & Bin Yu & Teófilo Valdés & Carlos Rivero & Jianqing Fan & Aad Vaart, 2006. "Regularization in statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 271-344, September.
    2. Rivero, Carlos & Valdes, Teofilo, 2008. "An algorithm for robust linear estimation with grouped data," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 255-271, December.

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