Publication: Analysis of variance with general errors and grouped and non-grouped data: Some iterative algorithms
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In this paper we consider some iterative estimation algorithms, which are valid to analyse the variance of data, which may be either non-grouped or grouped with different classification intervals. This situation appears, for instance, when data is collected from different sources and the grouping intervals differ from one source to another. The analysis of variance is carried out by means of general linear models, whose error terms may be general. An initial procedure in the line of the EM, although it does not necessarily agree with it, opens the paper and gives rise to a simplified version where we avoid the double iteration, which implicitly appears in the EM and, also, in the initial procedure mentioned above. The asymptotic stochastic properties of the resulting estimates have been investigated in depth and used to test ANOVA hypothesis
M.Y. An, Logconcavity versus logconvexity: A complete characterization, J. Econom. Theory 80 (1998) 350–369. A.P. Dempster, N.M. Laird, D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Soc. 39 B (1977) 1–22. M.J.R. Healy, M. Westmacott, Missing values in experiments analysed on automatic computers, Appl. Statist. 5 (1956) 203–206. C.R. Hicks, Fundamental Concepts in the Design of Experiments, Rinehart and Winston, Holt, 1973. R.G. Laha, V.K. Rohatgi, Probability Theory, Wiley, 1979. R.J.A. Little, D.B. Rubin, Statistical Analysis with Missing Data, Wiley, 1987. G.J. McLachlan, T. Krishnan, The EM Algorithm and Extensions, Wiley, 1997. T. Orchard, M.A. Woodbury, A missing information principle: Theory and applications, Proc. Math. Statist. Probab. (1972) 697–715. Univ. California Press, Berkeley. M.A. Tanner, Tools for Statistical Inference. Methods for the Exploration of Posterior Distributions and Likelihood Functions, Springer, 1993.