Robust estimates in generalized partially linear models
TLDR
In this article, a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model is introduced, where the data are modeled by $y_i|(\mathbf{x}_i,t_i)\sim F(cdot,\mu_i)$ withAbstract:
In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model, where the data are modeled by $y_i|(\mathbf{x}_i,t_i)\sim F(\cdot,\mu_i)$ with $\mu_i=H(\eta(t_i)+\mathbf{x}_i^{$\mathrm{T}$}\beta)$, for some known distribution function F and link function H. It is shown that the estimates of $\beta$ are root-n consistent and asymptotically normal. Through a Monte Carlo study, the performance of these estimators is compared with that of the classical ones.read more
Citations
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Robustified maximum likelihood estimation in generalized partial linear mixed model for longitudinal data.
Guoyou Qin,Zhong Yi Zhu +1 more
TL;DR: The proposed robust estimation of both mean and variance components in generalized partial linear mixed models based on the construction of robustified likelihood function performs better than those resulting from robust estimating equations involving conditional expectation.
Journal ArticleDOI
Joint asymptotics for semi-nonparametric regression models with partially linear structure
Guang Cheng,Zuofeng Shang +1 more
TL;DR: In this paper, a joint Bahadur representation is developed for semi-parametric regression models, where the Euclidean estimator and (pointwise) functional estimator jointly converge to a zero-mean Gaussian vector.
Journal ArticleDOI
Robust inference in generalized partially linear models
TL;DR: A new class of robust estimates for the smooth function @h, associated to the nonparametric component, and for the parameter @b, related to the linear one, is defined, based on a three-step procedure, where large values of the deviance or Pearson residuals are bounded through a score function.
Journal ArticleDOI
Robust group non-convex estimations for high-dimensional partially linear models
Mingqiu Wang,Guo-Liang Tian +1 more
TL;DR: In this article, the robust group selection for partially linear models when the number of covariates can be larger than the sample size is considered, and the non-convex penalty function is applied to achieve both goals of variable selection and estimation simultaneously, and polynomial splines to estimate the nonparametric component.
Journal ArticleDOI
Robust estimates in generalized partially linear single-index models
TL;DR: The generalized partly linear single-index model as discussed by the authors is a generalization of the well known generalized linear models that allow only for some predictors to be modeled linearly while others are modeled nonparametrically.
References
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Book
Generalized Linear Models
Peter McCullagh,John A. Nelder +1 more
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
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TL;DR: In this article, the authors define the Ball Sigma-Field and Measurability of Suprema and show that it is possible to achieve convergence almost surely and in probability.
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TL;DR: In this paper, the authors define a functional on Stochastic Processes as random functions and propose a uniform convergence of empirical measures in Euclidean spaces, based on the notion of convergence in distribution.
Journal ArticleDOI
Root-n-consistent semiparametric regression
TL;DR: In this article, a variable aleatoire (X,Z) dans #7B-R P ×#7b-R q is considered, and an estimateur generalisant l'estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur Z is constructed.