By D. A. Stephens, A. F. M. Smith (auth.), Prof. Dr. Wolfgang Härdle, Prof. Léopold Simar (eds.)
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1, the matrix of V is as construc ted. An elegant and efficient way of construc tion follows (vuv '] t ! 1+Vz1V~~V1z When tion can 1 Vh. 1 is construc ted be applied recursively. inverted -Wishar t matrices can an upper as triangul ar An algorithm be construc ted for generati ng this using the matrix, decompo si- square roots of decompo sition, see generate the Zellner, Bauwens and Van Dijk (1988). It square is course of roots of the also possible inverted -Wishar t as suggeste d random earlier, matrices as to inverses of square 40 of roots distributed random be calculated efficiently.
BAUWENS CORE, Universite Catholique de Louvain, 34 Voie du Roman Pays, 1348 Louvain-La-Neuve, BELGIUM A. RASOUERO GREQE, Ecole des Hautes Etudes en Sciences Sociales, 2 Rue de la Charite, 13002 Marseille, FRANCE Key Words: Residual Autocorrelation, Regression Model, Bayesian Inference. HPD Region, Power, Augmented Regressions, Abstract We evaluate two tests of residual autocorrelation in the linear regression model in a Bayesian framework. Each test checks if an approximate highest posterior density region of the parameters of the autoregressive process of the error contains the null hypothesis.
I) Since o is a non-linear function of e, the posterior density of o is not known analytically. 4) and calculate for each drawing the corresponding value of o. By simple averaging of these N values and of functions of them we can obtain (if N is large enough) a very good approximation of the posterior expectation E(o I y) and of the variance-covaria nce matrix V(o I y). The covariance matrix Cov(o,o: I y) can be computed likewise. E(o: I y) and V(o: I y) being known analytically, this step provides us with E(
Computer Intensive Methods in Statistics by D. A. Stephens, A. F. M. Smith (auth.), Prof. Dr. Wolfgang Härdle, Prof. Léopold Simar (eds.)