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

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. Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics..

A robust algorithm for the sequential linear analysis of environmental radiological data with imprecise observations

“…Although this point will be clarified in Section 6, let us advance that in the first case only first derivatives are involved, while with the ML techniques the second derivatives that form part of the Hessian of the log-likelihood do not admit an explicit expression and need to be numerically evaluated. These comments sum up the potentialities of the algorithm proposed in this paper, which has a direct antecedent in Rivero and Valdes (2004), as will be explained in the next section.…”

“…More recent bibliographical antecedents are James and Smith (1984), Ritov (1990) and Anido et al (2000). However, the direct precursor must undoubtedly be sought in Rivero and Valdes (2004) (Section 3,p. 471), where the authors suggest an estimating algorithm useful when the data are sequentially received and the scale parameter s of model (1) is assumed to be known.…”