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An algorithm for robust linear estimation with grouped data

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  • Rivero, Carlos
  • Valdes, Teofilo

Abstract

An algorithm which is valid to estimate the parameters of linear models under several robust conditions is presented. With respect to the robust conditions, firstly, the dependent variables may be either non-grouped or grouped. Secondly, the distribution of the errors may vary within the wide class of the strongly unimodal distributions, either symmetrical or non-symmetrical. Finally, the variance of the errors is unknown. Under these circumstances the algorithm is not only capable of estimating the parameters (slopes and error variance) of the linear model, but also the asymptotic covariance matrix of the linear parameters. This opens the possibility of making inferences in terms of either multiple confidence regions or hypothesis testing.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:255-271
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    References listed on IDEAS

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    1. Carmen Anido & Teófilo Valdés & Carlos Rivero, 2000. "Modal iterative estimation in linear models with unimodal errors and non-grouped and grouped data collected from different sources," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 393-416, December.
    2. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
    3. 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.
    4. Michael Healy & Michael Westmacott, 1956. "Missing Values in Experiments Analysed on Automatic Computers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 5(3), pages 203-206, November.
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    1. Blanco-Fernández, Angela & Corral, Norberto & González-Rodríguez, Gil, 2011. "Estimation of a flexible simple linear model for interval data based on set arithmetic," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2568-2578, September.

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