Copyright (c) 2008 All rights reserved. http://works.bepress.com/raymond_carroll Recent documents in Raymond J Carroll en-us Thu, 03 Jan 2008 14:14:45 PST 3600 http://works.bepress.com/raymond_carroll/2 http://works.bepress.com/raymond_carroll/2 Sat, 11 Nov 2006 08:28:57 PST An increasingly popular tool for nonparametric smoothing are penalized splines (P-splines) which use low-rank spline bases to make computations tractable while maintaining accuracy as good as smoothing splines. This paper extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. These extensions have been studied before, but never together and never in the multivariate case. This combination is needed for satisfactory inference and can be implemented effectively by Bayesian \mbox{MCMC}. The variance process controlling the spatially-adaptive shrinkage of the mean and the variance of the heteroscedastic error process are modeled as log-penalized splines. We discuss the choice of priors and extensions of the methodology,in particular, to multivariate smoothing using low-rank thin plate splines. A fully Bayesian approach provides the joint posterior distribution of all parameters, in particular, of the error standard deviation and penalty functions. In the multivariate case we produce maps of the standard deviation and penalty functions. Our methodology can be implemented using the Bayesian software WinBUGS. Ciprian M. Crainiceanu Computation Multivariate Analysis Statistical Models http://works.bepress.com/raymond_carroll/1 http://works.bepress.com/raymond_carroll/1 Sat, 11 Nov 2006 08:28:55 PST This paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function. Special cases in our approach include marginal models for longitudinal/clustered data, conditional logistic regression for matched case-control studies, multivariate measurement error models, generalized linear mixed models with a semiparametric component, and many others. We propose profile-kernel and backfitting estimation methods for these problems, derive their asymptotic distributions, and show that in likelihood problems the methods are semiparametric efficient. While generally not true, with our methods profiling and backfitting are asymptotically equivalent. We also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm. The proposed methods are evaluated using simulation studies and applied to the Kenya hemoglobin data. Xihong Lin Longitudinal Data Analysis and Time Series Multivariate Analysis Statistical Theory and Methods http://works.bepress.com/raymond_carroll/3 http://works.bepress.com/raymond_carroll/3 Sat, 11 Nov 2006 08:28:06 PST Raymond J. Carroll Longitudinal Data Analysis and Time Series