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

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Anido, Carmen and Valdés Sánchez, Teófilo and Rivero, Carlos (2000) Modal iterative estimation in linear models with unimodal errors and non-grouped and grouped data collected from different sources. Test, 9 (2). pp. 393-416. ISSN 1133-0686

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Official URL: http://link.springer.com/content/pdf/10.1007%2FBF02595742


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Abstract

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 an M-estimator, may enjoy good stochastic asymptotic properties such as consistency, boundness in L-2, and limit normality


Item Type:Article
Uncontrolled Keywords:Censored-data; maximum-likelihood; em algorithm; regression; asymptotic distributions; consistency; convergence rate; grouped data; imputation; iterative estimation; linear models
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:20229
Deposited On:04 Mar 2013 15:59
Last Modified:09 Aug 2018 08:38

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