In variational data assimilation, optimal ingestion of the observational data and optimal use of prior physical and statistical information involve the choice of numerous weighting, smoothing and tuning parameters which control the ltering and merging of divers sources of information. Generally these weights must be obtained from a partial and imperfect understanding of various sources of error...

An extension of reproducing kernel Hilbert space (RKHS) theory provides a new framework for modeling functional regression models with functional responses. The approach only presumes a general nonlinear regression structure as opposed to previously studied linear regression models. Generalized cross-validation (GCV) is proposed for automatic smoothing parameter estimation. The new RKHS estimat...

It has been shown that space-variant regularization in image restoration provides better results than space-invariant regularization. However, the optimal choice of the regularization parameter is usually unknown a priori. In previous work, the generalized cross-validation (GCV) criterion was shown to provide accurate estimates of the optimal regularization parameter. The author introduces a mo...

We propose new approaches for choosing the shrinkage parameter in ridge regression, a penalized likelihood method for regularizing linear regression coefficients, when the number of observations is small relative to the number of parameters. Existing methods may lead to extreme choices of this parameter, which will either not shrink the coefficients enough or shrink them by too much. Within thi...

To enhance the efficacy of ganciclovir/herpes simplex virus thymidine kinase (GCV/HSV-TK) suicide gene therapy for nasopharyngeal cancer KB, we developed long-circulating liposome-encapsulated GCV, and evaluated cytotoxicity in vitro and in vivo. PEGylated liposome-encapsulated GCV (PEG-GCV-lipo) was prepared by the freeze-thawing method. In vitro experiments demonstrated that GCV from liposome...

This paper concerns the asymptotic properties of a class of criteria for model selection in linear regression models, which covers the most well known criteria as e.g. MALLOWS' Cp, CV (cross-validation), GCV ( generalized cross-validation), AKAIKE's AIC and FPE as well as SCHWARZ' BIC. These criteria are shown to be consistent in the sense of selecting the true or larger models, assuming i.i.d....

This article considers spline smoothing of variance functions. We focus on selection of smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross validation (GACV) and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, genera...

In this paper, we propose a numerical algorithm for filtering and robust signal differentiation. The numerical procedure is based on the solution of a simplified linear optimization problem. A compromise between smoothing and fidelity with respect to the measurable data is achieved by the computation of an optimal regularization parameter that minimizes the Generalized Cross Validation criterio...