## Spline estimation of single-index models

(2013). Spline-based semiparametric estimation of partially linear Poisson regression with single-index models. Journal of Nonparametric Statistics: Vol. 25, No. 4, pp. 905-922. Estimation of Single-Index Models Based on Boosting Techniques Florian Leitenstorfer & Gerhard Tutz Ludwig-Maximilians-UniversitÄat MuncÄ hen Akademiestra¼e 1, 80799 MuncÄ hen ftutz, leiten g@stat.uni-muenchen.de June 19, 2008 Abstract In single-index models the link or response function is not considered as ¯xed. Abstract. We consider spline-based quasi-likelihood estimation for mixed Poisson regression with single-index models. The unknown smooth function is approximated by B-splines, and a modified Fisher scoring algorithm is employed to compute the estimates.The spline estimate of the nonparametric component is shown to achieve the optimal rate of convergence, and the asymptotic normality of the

25 Apr 2017 Title Constrained Single Index Model Estimation. Type Package An Algorithm for Computing Constrained Smoothing Spline. Functions. 31 Jan 2019 Smoothing splines in partially linear single-index-coefficient model. Suppose that the data (Xi, Z1i, Z2i, Y  sion models, most notably additive models or single index models, as special cases the usual smoothing spline estimate of the additive model. (Wahba, 1990). 1.2 The single index models with homogeneity structure if the homogeneity pursuit is conducted, we only need to estimate H1, much smaller than m, We use the B-Spline basis of order s in this paper, and the basis, B(·), is formed by the. (2011) proposed to estimate the nonparametric components by polynomial splines (Stone, 1986, 1994). After the spline basis is  partially linear models and single index models The single index model is defined as: B # 2 ,p! Spline estimation is sensitive to the choice of the number of. 31 Jul 2014 Abstract We propose a functional single-index model (FSiM) to study functional predictors are observed at discrete points, we use B-spline

## SPLINE ESTIMATION OF SINGLE-INDEX MODELS Li Wang and Lijian Yang University of Georgia and Michigan State University Supplementary Material This note contains proofs for the main results. The following two propo-sitions play an important role in the proof. Proposition A.1 establishes the uniform convergence rate of the derivatives of ˆγ

In this paper, we investigate general single-index models (SIMs) in high dimensions. Based on. U-statistics, we propose two types of robust es- timators for the  In a semiparametric single index model, the object of interest depends on x The leave#one#out version is used since we are estimating the regression at the   SPLINE ESTIMATION OF SINGLE-INDEX MODELS Li Wang and Lijian Yang University of Georgia and Michigan State University Abstract: For the past two decades, the single-index model, a special case of pro-jection pursuit regression, has proven to be an eﬃcient way of coping with the high-dimensional problem in nonparametric regression. SPLINE ESTIMATION OF SINGLE-INDEX MODELS Li Wang and Lijian Yang University of Georgia and Michigan State University Abstract: For the past two decades, the single-index model, a special case of pro jection pursuit regression, has proven to be an efficient way of coping with the high-dimensional problem in nonparametric regression. For the past two decades, the single-index model, a special case of pro- jection pursuit regression, has proven to be an efficient way of coping with the high-dimensional problem in nonparametric regression. In this paper, based on a weakly dependent

### Estimation of Single-Index Models Based on Boosting Techniques Florian Leitenstorfer & Gerhard Tutz Ludwig-Maximilians-UniversitÄat MuncÄ hen Akademiestra¼e 1, 80799 MuncÄ hen ftutz, leiten g@stat.uni-muenchen.de June 19, 2008 Abstract In single-index models the link or response function is not considered as ¯xed.

8 Jan 2013 Yu, Y, Ruppert, D. Penalized spline estimation for partially linear single-index models. J Am Stat Assoc 2002; 974601042–1054. 25 Apr 2017 Title Constrained Single Index Model Estimation. Type Package An Algorithm for Computing Constrained Smoothing Spline. Functions. 31 Jan 2019 Smoothing splines in partially linear single-index-coefficient model. Suppose that the data (Xi, Z1i, Z2i, Y  sion models, most notably additive models or single index models, as special cases the usual smoothing spline estimate of the additive model. (Wahba, 1990). 1.2 The single index models with homogeneity structure if the homogeneity pursuit is conducted, we only need to estimate H1, much smaller than m, We use the B-Spline basis of order s in this paper, and the basis, B(·), is formed by the. (2011) proposed to estimate the nonparametric components by polynomial splines (Stone, 1986, 1994). After the spline basis is  partially linear models and single index models The single index model is defined as: B # 2 ,p! Spline estimation is sensitive to the choice of the number of.

### 30 Nov 2016 In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth link function.

SPLINE ESTIMATION OF SINGLE-INDEX MODELS Li Wang and Lijian Yang University of Georgia and Michigan State University Abstract: For the past two decades, the single-index model, a special case of pro jection pursuit regression, has proven to be an efficient way of coping with the high-dimensional problem in nonparametric regression. SPLINE ESTIMATION OF SINGLE-INDEX MODELS Li Wang and Lijian Yang University of Georgia and Michigan State University Supplementary Material This note contains proofs for the main results. The following two propo-sitions play an important role in the proof. Proposition A.1 establishes the uniform convergence rate of the derivatives of ˆγ In this paper, based on a weakly dependent sample, we investigate a robust single-index model, where the single-index is identified by the best approximation to the multivariate prediction function of the response variable, regardless of whether the prediction function is a genuine single-index function. A polynomial spline estimator is (2013). Spline-based semiparametric estimation of partially linear Poisson regression with single-index models. Journal of Nonparametric Statistics: Vol. 25, No. 4, pp. 905-922. Estimation of Single-Index Models Based on Boosting Techniques Florian Leitenstorfer & Gerhard Tutz Ludwig-Maximilians-UniversitÄat MuncÄ hen Akademiestra¼e 1, 80799 MuncÄ hen ftutz, leiten g@stat.uni-muenchen.de June 19, 2008 Abstract In single-index models the link or response function is not considered as ¯xed. Abstract. We consider spline-based quasi-likelihood estimation for mixed Poisson regression with single-index models. The unknown smooth function is approximated by B-splines, and a modified Fisher scoring algorithm is employed to compute the estimates.The spline estimate of the nonparametric component is shown to achieve the optimal rate of convergence, and the asymptotic normality of the

## sion models, most notably additive models or single index models, as special cases the usual smoothing spline estimate of the additive model. (Wahba, 1990).

1.2 The single index models with homogeneity structure if the homogeneity pursuit is conducted, we only need to estimate H1, much smaller than m, We use the B-Spline basis of order s in this paper, and the basis, B(·), is formed by the. (2011) proposed to estimate the nonparametric components by polynomial splines (Stone, 1986, 1994). After the spline basis is  partially linear models and single index models The single index model is defined as: B # 2 ,p! Spline estimation is sensitive to the choice of the number of.

31 Jan 2019 Smoothing splines in partially linear single-index-coefficient model. Suppose that the data (Xi, Z1i, Z2i, Y  sion models, most notably additive models or single index models, as special cases the usual smoothing spline estimate of the additive model. (Wahba, 1990). 1.2 The single index models with homogeneity structure if the homogeneity pursuit is conducted, we only need to estimate H1, much smaller than m, We use the B-Spline basis of order s in this paper, and the basis, B(·), is formed by the. (2011) proposed to estimate the nonparametric components by polynomial splines (Stone, 1986, 1994). After the spline basis is  partially linear models and single index models The single index model is defined as: B # 2 ,p! Spline estimation is sensitive to the choice of the number of.