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...

Markov state models are a widely used method for approximating the eigenspectrum of the molecular dynamics propagator, yielding insight into the long-timescale statistical kinetics and slow dynamical modes of biomolecular systems. However, the lack of a unified theoretical framework for choosing between alternative models has hampered progress, especially for non-experts applying these methods ...

Transmission of zoonotic cutaneous leishmaniasis (ZCL) depends on the presence, density and distribution of Leishmania major rodent reservoir and the development of these rodents is known to have a significant dependence on environmental and climate factors. ZCL in Tunisia is one of the most common forms of leishmaniasis. The aim of this paper was to build a regression model of ZCL cases to ide...

Efficient algorithms that compute both the estimates and the generalized cross-validation score for the problem of Whittaker– Henderson smoothing are presented. Algorithm efficiency results from carefully exploiting the problem’s rich structure to reduce execution time and memory use. The algorithms are much faster than existing ones, and use significantly less memory. MATLAB M-files are includ...

Inverse problems are usually ill-posed in such a way that it is necessary to use some method to reduce their deficiencies. The method that we choose is the regularization by derivative matrices. There is a crucial problem in regularization, which is the selection of the regularization parameter λ. In this work we use generalized cross validation (GCV) as a tool for the selection of λ. GCV was p...

[1] Estimating CO2 fluxes from the pattern of atmospheric CO2 concentrations with atmospheric transport models is an ill-posed inverse problem, whose solution is stabilized using prior information. Weights assigned to prior information and to CO2 concentrations at different locations are quantified by parameters that are not well known, and differences in the choice of these parameters contribu...

This paper considers optimization of the ridge parameters in generalized ridge regression (GRR) by minimizing a model selection criterion. GRR has a major advantage over ridge regression (RR) in that a solution to the minimization problem for one model selection criterion, i.e., Mallows’ Cp criterion, can be obtained explicitly with GRR, but such a solution for any model selection criteria, e.g...

The choice of the optimal spherical radial basis function (SRBF) in local gravity field modelling from terrestrial gravity data is investigated. Various types of SRBFs are considered: the point-mass kernel, radial multipoles, Poisson wavelets, and the Poisson kernel. The analytical expressions for the Poisson kernel, the point-mass kernel and the radial multipoles are well known, while for the ...

In this paper we address the problem of approximating functions on a semi-in nite interval by truncated series of orthonormal generalized Laguerre functions. The generalized Laguerre functions contain two parameters, namely a scale factor and an order of generalization. The rate of convergence of a generalized Laguerre series depends on the choice of these parameters. Results concerning the det...