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Computer Intensive Methods in Statistics by D. A. Stephens, A. F. M. Smith (auth.), Prof. Dr. Wolfgang

By D. A. Stephens, A. F. M. Smith (auth.), Prof. Dr. Wolfgang Härdle, Prof. Léopold Simar (eds.)

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The functions is defined through the transfor- (C~uchy) mation function t = zv! and the t density is defined as the marginal density of an uncountable mixture of conditional normal densities with an inverted density as i in statistics as mixing density. For details we refer to textbooks Raiffa and Schlaiffer (1961, pp. 232-233). A nonstandard t distribution may be defined through a linear transformation which function For instance, let t - changes t( the location and scale of the 0, 1, A) then t * = buted random variable with location parameter It follows from directly the is trivial.

Special weights are attached to each random drawing of the reduced form parameters to assure that 46 posterior joint the SEM likelihood. These jacobian of the the of weights transformation have a formal proportional theoretic ground structural from is parameters form structural form to and reduced to the equal the form. The resulting posteriors of the structural form do not confirm very well with the tors. As a of of the pdf's consequence the application normality asymptotic the of classical structural asymptotic theory form seems estimarather restrictive for several SEM's.

93 0. 14 44 45 The posterior means and standard deviations of the structural form parameters (defined on a truncated parameter region) and the classical estimates of these parameters of both meat market models are shown in table 1. Table Posterior means and classical estimates 1. S) df the parameters of the Tintner and BBM models (stand. dev. 28 0. 1 8 1. 18 0. 13 0. 36 0. 06 0. 81 1. 27 0. 15 0. 69 0. 11 0. 05 0. 07 0. 11 between the posterior means of the structural The differences meters and the classical estimates is quite substantial for form parathe Tintner model.

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