In this paper penalized weighted least-squares is used to jointly estimate nonparametric functions from contemporaneously correlated data. Under conditions generally encountered in practice, it is shown that these joint estimates have smaller posterior variances than those of marginal estimates and are therefore more efficient. We describe three methods: generalized maximum likelihood (GML), ge...

It is shown that the basic regularization procedures for finding meaningful approximate solutions of ill-conditioned or singular linear systems can be phrased and analyzed in terms of classical linear algebra that can be taught in any numerical analysis course. Apart from rewriting many known results in a more elegant form, we also derive a new two-parameter family of merit functions for the de...

In this paper‎, two inverse problems of determining an unknown source term in a parabolic‎ equation are considered‎. ‎First‎, ‎the unknown source term is ‎estimated in the form of a combination of Chebyshev functions‎. ‎Then‎, ‎a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem‎. ‎For solving the problem‎, ‎the operational matrices of int...

We discuss a flexible method for modeling survival data using penalized smoothing splines when the values of covariates change for the duration of the study. The Cox proportional hazards model has been widely used for the analysis of treatment and prognostic effects with censored survival data. However, a number of theoretical problems with respect to the baseline survival function remain unsol...

Generalized cross validation (GCV) is one of the most important approaches used to estimate parameters in the context of inverse problems and regularization techniques. A notable example is the determination of the smoothness parameter in splines. When the data are generated by a state space model, like in the spline case, efficient algorithms are available to evaluate the GCV score with comple...

Cross-validation is a tried and tested approach to select the number of components in principal component analysis (PCA), however, its main drawback is its computational cost. In a regression (or in a non parametric regression) setting, criteria such as the general cross-validation one (GCV) provide convenient approximations to leave-one-out crossvalidation. They are based on the relation betwe...

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...

In some cases of regression modeling, it is very common to find a repeating pattern. To model this, course, the approach used must be in accordance with characteristics data. The Fourier series one proposed approaches, because has advantages modeling relationship patterns that tend repeat, such as cosine sine waves. subset nonparametric regression, which good flexibility modeling. this study, w...

Linear parametric regression models of fMRI time series have correlated residuals. One approach to address this problem is to condition the autocorrelation structure by temporal smoothing. Smoothing splines with the degree of smoothing selected by generalized cross-validation (GCV-spline) provide a method to find an optimal smoother for an fMRI time series. The purpose of this study was to dete...

Gaussian processes are powerful regression models specified by parameterized mean and covariance functions. Standard approaches to choose these parameters (known by the name hyperparameters) are maximum likelihood and maximum a posteriori. In this article, we propose and investigate predictive approaches based on Geisser's predictive sample reuse (PSR) methodology and the related Stone's cross-...