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We introduce a generalized Crofoot transform between the model spaces corresponding to matrix-valued inner functions. As an application, we obtain results about truncated Toeplitz operators.

Generalized additive models (GAMs) have become an elegant and practical option in model building. Estimation of a smooth GAM component traditionally requires an algorithm that cycles through and updates each smooth, while holding other components at their current estimated fit, until specified convergence. We aim to fit all the smooth components simultaneously. This can be achieved using penali...

Model selection is a necessary step in many practical regression analyses. But for methods based on estimating equations, such as the quasi-likelihood and generalized estimating equation (GEE) approaches, there seem to be few well-studied model selection techniques. In this article, we propose a new model selection criterion that minimizes the expected predictive bias (EPB) of estimating equati...

a reliable quantitative structure retention relationship (qsrr) study has been evaluated to predict the retention indices (ris) of a broad spectrum of compounds, namely 118 non-linear, cyclic and heterocyclic terpenoids (both saturated and unsaturated), on an hp-5ms fused silica column. a principal component analysis showed that seven compounds lay outside of the main cluster. after elimination...

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...

We present an efficient algorithm for simultaneously training sparse generalized linear models across many related problems, which may arise from bootstrapping, cross-validation and nonparametric permutation testing. Our approach leverages the redundancies across problems to obtain significant computational improvements relative to solving the problems sequentially by a conventional algorithm. ...