In this article, we propose to estimate the regression parameters in a semiparametric generalized linear model by moment estimating equations. These estimators are shown to be consistent and asymptotically normal. We present two estimators of the nonparametric part, provide conditions for the existence and uniform consistency, and obtain faster rates of convergence under weaker assumptions.

In the paper we propose nonparametric approaches for elearning data. In particular we want to supply a measure of the relative exercises importance, to estimate the acquired Knowledge for each student and finally to personalize the e-learning platform. The methodology employed is based on a comparison between nonparametric statistics for kernel density classification and parametric models such ...

| In the class of hierarchical mixtures-of-experts (HME) models, \experts" in the exponential family with generalized linear mean functions of the form (+ x T) are mixed, according to a set of local weights called the \gating functions" depending on the predictor x. Here () is the inverse link function. We provide regularity conditions on the experts and on the gating functions under which the ...

In this paper, empirical likelihood-based inference for longitudinal data within the framework of generalized linear model is investigated. The proposed procedure takes into account the within-subject correlation without involving direct estimation of nuisance parameters in the correlation matrix and retains optimal even if the working correlation structure is misspecified. The proposed approac...

Abstract—A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some ...

Received: 22 August 2007 / Revised: 7 April 2008 c ©2008 Springer Science + Business Media, LLC Abstract In generalized linear models with fixed design, under the assumption λn → ∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator β̂n, which is the root of the quasi-likelihood equation with natural link function ∑n i=1 Xi(yi−μ(X ′ iβ)) = 0, is obtain...

It is often asserted that deep networks learn “features”, traditionally expressed by the activations of intermediate nodes. We explore an alternative concept by defining features as partial derivatives of model output with respect to model parameters—extending a simple yet powerful idea from generalized linear models. The resulting features are not equivalent to node activations, and we show th...

To obtain efficient estimation of parameters is a major objective in population pharmacokinetic study. In this paper, we propose an empirical likelihood-based method to analyze the population pharmacokinetic data based on the generalized linear model. A nonparametric version of the Wilk’s theorem for the limiting distributions of the empirical likelihood ratio is derived. Simulations are conduc...