Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace approximation to the full problem. Determination of the regularization parameter for the projected problem by unbiased predictive risk estimation, generalized...

an alumina supported co/ni catalyst was prepared by sol-gel procedure to study the catalytic behavior during fischer-tropsch synthesis in a fixed-bed reactor. the effect of co conversion (10-50%) on hydrocarbon product distribution (ch4, c5+ and c2-c4 olefin selectivities) was studied. selectivity for ch4 decreased, while those of c5+ and olefin selectivities increased with increasing co conver...

This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the cone and its dual nonnegative polynomials. By technique homogenization, give a convergent hierarchy Moment-SOS relaxations for approximating these cones. With them, method solving Finitely atomic representing measures, or certificates their nonexistence, can be obtained by p...

This paper introduces measures of information for Bayesian analysis when the support of data distribution is truncated progressively. The focus is on the lifetime distributions where the support is truncated at the current age t>=0. Notions of uncertainty and information are presented and operationalized by Shannon entropy, Kullback-Leibler information, and mutual information. Dynamic updatings...

Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with parametric random effects and flexible fixed effects, and employ the penalized least squares method to estimate the models. The issue to be addressed is the s...

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...

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...

Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O.n3/, n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approxi...