Oracally Efficient Two-Step Estimation of Generalized Additive Model Rong Liu a b , Lijian Yang a c & Wolfgang K. Härdle d a Center for Advanced Statistics and Econometrics Research , Soochow University , China b Department of Mathematics and Statistics , University of Toledo , Toledo , OH , 43606 c Department of Statistics and Probability , Michigan State University , East Lansing , MI , 48824...

In many situations, data follow a generalized partly linear model in which the mean of the responses is modeled, through a link function, linearly on some covariates and nonparametrically on the remaining ones. A new class of robust estimates for the smooth function η, associated to the nonparametric component, and for the parameter β, related to the linear one, is defined. The robust estimator...

Canonical generalized linear models (GLM) are specified by a finite dimensional vector and a monotonically increasing function called the link function. Standard parameter estimation techniques hold the link function fixed and optimizes over the parameter vector. We propose a parameter-recovery facilitating, jointly-convex, regularized loss functional that is optimized globally over the vector ...

| 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...

Christoffersen, Jacobs, and Ornthanalai (2012) (CJO) propose an interesting and useful class of generalized autoregressive conditional heteroskedasticity (GARCH)-like models with dynamic jump intensity, and find evidence that the models not only fit returns data better than some commonly used benchmarks but also provide substantial improvements in option pricing performance. While such models p...

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 ...

In this study, per-person municipal expenditures were modeled as a function of six demographic and income-related variables, first using a robust linear regression model (LM), and second using a generalized additive model (GAM). A comparison of the two models revealed that the GAM provided more accurate predictions, and therefore we recommend for the client to use the GAM as the basis for predi...

This note describes ANOVAs and how they can be implemented in SPM. For each type of ANOVA we show what are the relevant statistical models and how they can be implemented in a GLM. We give examples of how main effects and interactions can be tested for using F-contrasts in SPM. We also show how to implement a repeated-measures M-way ANOVA with partitioned errors using a two-level procedure in SPM.

Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation mod...