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Efficient Estimation in Single Index Models through Smoothing splines
TLDR
In this paper, the authors developed a method to compute the penalized least squares estimators (PLSEs) of the parametric and nonparametric components given independent and identically distributed (i.i.d.) data.Abstract:
We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth link function. We develop a method to compute the penalized least squares estimators (PLSEs) of the parametric and the nonparametric components given independent and identically distributed (i.i.d.)~data. We prove the consistency and find the rates of convergence of the estimators. We establish asymptotic normality under under mild assumption and prove asymptotic efficiency of the parametric component under homoscedastic errors. A finite sample simulation corroborates our asymptotic theory. We also analyze a car mileage data set and a Ozone concentration data set. The identifiability and existence of the PLSEs are also investigated.read more
Citations
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Journal ArticleDOI
Score estimation in the monotone single-index model
TL;DR: This work considers estimation in the single‐index model where the link function is monotone and shows how one can solve this score equation without any reparametrization, which makes it easy to solve the score equations in high dimensions.
Book ChapterDOI
Profile Least Squares Estimators in the Monotone Single Index Model
TL;DR: In this paper, a profile least squares estimator was proposed to estimate a fixed regression parameter in a monotone single index regression model, which is shown to be convergence and asymptotic normal.
Journal ArticleDOI
Estimating covariance and precision matrices along subspaces
Željko Kereta,Timo Klock +1 more
TL;DR: The results show that the estimation accuracy depends almost exclusively on the components of the distribution that correspond to desired subspaces or directions, relevant and important for problems where the behavior of data along a lower-dimensional space is of specific interest, such as dimension reduction or structured regression problems.
Posted Content
Least Squares Estimation in a Single Index Model with Convex Lipschitz link
TL;DR: In this paper, a Lipschitz constrained least squares estimator (LLSE) for both the parametric and the nonparametric components given independent and identically distributed observations is proposed.
References
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Journal ArticleDOI
A single-index model with multiple-links.
TL;DR: This paper presents a parsimonious generalization of the single- index models that targets the effect of the interaction between the treatment conditions and the vector of covariates on the outcome, a single-index model with multiple-links (SIMML) that estimates a single linear combination of the covariates (i.e., asingle-index), with treatment-specific nonparametric link functions.
Journal ArticleDOI
Efficient estimation for generalized partially linear single-index models
Li Wang,Guanqun Cao +1 more
TL;DR: In this article, an efficient and practical approach to estimate the single-index link function, single index coefficients as well as the coefficients in the linear component of the model was proposed.
Journal ArticleDOI
A new minimum contrast approach for inference in single-index models
Weiyu Li,Valentin Patilea +1 more
TL;DR: A new, general inference approach is proposed for single-index models, based on a quadratic form criterion involving kernel smoothing, which could be applied with general single- index assumptions, in particular for mean regression models and conditional law models.
Journal ArticleDOI
Efficient estimation and computation of parameters and nonparametric functions in generalized semi/non-parametric regression models
TL;DR: In this paper, a maximum likelihood principle combined with the local linear technique was proposed for estimating the parameters and nonparametric functions in a class of generalized semi/nonparametric regression models, which cover commonly used semi-parametric models such as partially linear models, partially linear single index models, and two-sample semiparametric models.
Journal ArticleDOI
On quasi-inversions
TL;DR: In this paper, a quasi-inversion of the chordal metric was shown to be bi-Lipschitz w.r.t if and only if every "tangent line" is far away from the origin.
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