, Volume 9, Issue 2, pp 393–416 | Cite as

Modal iterative estimation in linear models with unimodal errors and non-grouped and grouped data collected from different sources

  • Carmen AnidoEmail author
  • Teófilo Valdés
  • Carlos Rivero


In this paper we introduce an iterative estimation procedure based on conditional modes suitable to fit linear models when errors are known to be unimodal and, moreover, the dependent data stem from different sources and, consequently, may be either non-grouped or grouped with different classification criteria. The procedure requires, at each step, the imputation of the exact values of the grouped data and runs by means of a process that is similar to the EM algorithm with normal errors. The expectation step has been substituted with a mode step that avoids awkward integration with general errors and, in addition, we have substituted the maximisation step with a natural one which only coincides with it when the error distribution is normal. Notwithstanding the former modifications, we have proved that, on the one hand, the iterative estimating algorithm converges to a point which is unique and non-dependent on the starting values and, on the other hand, our final estimate, being anM-estimator, may enjoy good stochastic asymptotic properties such as consistency, boundness inL 2, and limit normality.

Key Words

Asymptotic distributions consistency convergence rate grouped data imputation iterative estimation linear models 

AMS subject classification



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Copyright information

© Sociedad Española de Estadistica e Investigación Operativa 2000

Authors and Affiliations

  1. 1.Departmento de Estadística e Investigación OperativaUniversidad Complutense de MadridSpain
  2. 2.Departamento de Análisis Económico: Economía Cuantitativa, Facultad de Económicas y EmpresarialesUniversidad Autónoma de MadridMadridSpain

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