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Bayesian measures of model complexity and fit
 Journal of the Royal Statistical Society, Series B
, 2002
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[Read before The Royal Statistical Society at a meeting organized by the Research
Nonparametric Smoothing Using State Space Techniques
"... The authors examine the equivalence between penalized least squares and state space smoothing using random vectors with infinite variance. They show that despite infinite variance, many time series techniques for estimation, significance testing, and diagnostics can be used. The Kalman filter can be ..."
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The authors examine the equivalence between penalized least squares and state space smoothing using random vectors with infinite variance. They show that despite infinite variance, many time series techniques for estimation, significance testing, and diagnostics can be used. The Kalman filter can be used to fit penalized least squares models, computing the smoothed quantities and related values. Infinite variance is equivalent to di#erencing to stationarity, and to adding explanatory variables. The authors examine constructs called "smoothations" which they show to be fundamental in smoothing. Applications illustrate concepts and methods. R ESUM E Les auteurs examinent l'equivalence entre les moindres carres penalises et le lissage de l'espace d'etats au moyen de vecteurs aleatoires a variance infinie. Ils montrent que malgre le probleme de variance infinie, plusieurs techniques de diagnostic, d'estimation et de test de signification propres aux chroniques restent valables. Le filt...
Purpose Purpose and Description
"... These Fortran77 subroutines provide tools for penalized likelihood estimation and model checking for generalized linear models (GLMs) in which the model has a semiparametric form. The routines build on GCVPACK (Bates et al., 1987) and are designed to use the generalized crossvalidation criteria ( ..."
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These Fortran77 subroutines provide tools for penalized likelihood estimation and model checking for generalized linear models (GLMs) in which the model has a semiparametric form. The routines build on GCVPACK (Bates et al., 1987) and are designed to use the generalized crossvalidation criteria (Craven and Wahba. 1979) to determine the degree of data smoothing. 'Ihese problems include smoothed GLMs (O'Sullivan, YandeU and Raynor, 1986). iteratively reweighted least squares (Green, 1984), and general nonlinear problems. We present some of the problems PGLMPACK is designed for and describe the structure of the routines. General Problem: A variety of penalized nonlinear problems can be solved by an iterative scheme in which the inner step involves a linear model approximation. with J = bI...,y.)T the working values. 8 = (el,.. the linearized model and E = (E~,..,E,,) ~ a random vector with zero mean and covariance w', which is often diagonal. m e matrix W is referred to as the working weights.) In many situation, a semiparametric model is appropriate, such as in which si is a cvector of covariales with corresponding parameter vector a, xi is a dvector of variates and f (.) is some "smooth " function. Smoothness can be enforced by a "roughness
& Gynecology)
"... ❙ X: Επίπεδο εστριόλης (estriol) των εγκύων γυναικών ❚ Υ i ~ Normal(μ i, σ 2) ❚ μ i =η i =α+βΧ i 6 … ΑΠΛΟΙ ΕΛΕΓΧΟΙ ΥΠΟΘΕΣΕΩΝ 6.1. Εισαγωγή: ΕκτωνΥστερων Λόγος ..."
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❙ X: Επίπεδο εστριόλης (estriol) των εγκύων γυναικών ❚ Υ i ~ Normal(μ i, σ 2) ❚ μ i =η i =α+βΧ i 6 … ΑΠΛΟΙ ΕΛΕΓΧΟΙ ΥΠΟΘΕΣΕΩΝ 6.1. Εισαγωγή: ΕκτωνΥστερων Λόγος
ALGORITHMS FOR MULTIDIMENSIONAL SEMIPARAMETRIC GLM'S
, 1988
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