Single index models parametric
function form of E (Y| X), the parametric single index model can lead to more accurate estimates, especially when the dimension p of X is high, provided that the model is correctly built. We consider nonlinear heteroscedastic single-index models where the mean function is a parametric nonlinear model and the variance function depends on a single-index structure. Due to the semi-parametric nature of the single-index model, it is not helpful to further decompose Π N T 2 as Π N T 2 = 1 N T ∑ i = 1 N ψ 1 i [θ o, g ˆ k (1)] ′ M F ˆ (F o − F ˆ Q − 1) γ o, i, where Q is given in Lemma 3.1. This is because further decomposing F o − F ˆ Q − 1 will introduce the residual O P (‖ (θ ˆ, g ˆ k) − (θ o, g o) ‖ w) into the system. If specified as a vector, then additional arguments will need to be supplied as necessary to specify the bandwidth type, kernel types, and so on. method. the single index model method, one of either “ichimura” (default) (Ichimura (1993)) or “kleinspady” (Klein and Spady (1993)). Defaults to ichimura. LDA and logistic regression model are parametric models. Both models require a few assumptions on the data collected. To make less assumptions, non-parametric or semi-parametric models could be used. To control model complexity, single index model is a great choice for semi-parametric models (Powell et al.,1989;Klein and Spady,1993;Ichimura, 1993). The literature on the estimation of semiparametric single-index models is extensive. The most popular estimation methods include averaged derivatives [Hardle and Stoker, 1989], sliced inverse¨ regression [Li, 1991] and semiparametric least squares [Ichimura, 1993]. Single index models The single index model is de–ned as: y = g(Xβ)+ε Advantage 1: generalizes the linear regression model (which assumes g() is linear) Advantage 2: the curse of dimensionality is avoided as there is only one nonparametric dimension Vincenzo Verardi Semiparametric regression 12/09/2013 3 / 66
To incorporate flexible nonlinear relationship between covariates and transformed failure times, we propose partially linear single index models to facilitate complex relationship between transformed failure times and covariates. We develop two inference methods which handle the unknown nonlinear function in the model from different perspectives.
In this paper, based on certain residual‐marked empirical processes, we study the model test to validate the composite structure with a given link function for parametric single‐index time series m The single index model of the previous sections has been extended to multiple index models in various ways. For instance, popular parametric models for data with multicategorical response variables (representing the choice of individuals among more than two alternatives) are of the multi-index form. Model checks for regression: an innovation process approach Stute, Winfried, Thies, Silke, and Zhu, Li-Xing, The Annals of Statistics, 1998 Exploring the constant coefficient of a single-index variation Zhang, Jun, Niu, Cuizhen, and Li, Gaorong, Brazilian Journal of Probability and Statistics, 2019 A robust and efficient estimation method for single index models to estimate both nonparametric and parametric parts of the single index model . We discuss asymptotic properties of the proposed estimators and show the proposed estimator is more efficient than the local linear regression (LLR) estimator based on least squares when there are To incorporate flexible nonlinear relationship between covariates and transformed failure times, we propose partially linear single index models to facilitate complex relationship between transformed failure times and covariates. We develop two inference methods which handle the unknown nonlinear function in the model from different perspectives. Variable selection and estimation for semi-parametric multiple-index models Wang, Tao, Xu, Peirong, and Zhu, Lixing, Bernoulli, 2015 A dimension reduction based approach for estimation and variable selection in partially linear single-index models with high-dimensional covariates Zhang, Jun, Wang, Tao, Zhu, Lixing, and Liang, Hua, Electronic Journal of Statistics, 2012 Title: Least Squares Estimation in a Single Index Model with Convex Lipschitz link Authors: Arun K. Kuchibhotla , Rohit K. Patra , Bodhisattva Sen (Submitted on 1 Aug 2017 ( v1 ), last revised 31 Aug 2018 (this version, v3))
26 Nov 2015 However, if the parametric single‐index model is not correctly fitted for the data, we must apply some other more flexible regression models;
Compared with nonparametric regression models that do not specify the function form of E(Y |X), the parametric single index model can lead to more accurate 26 Nov 2015 However, if the parametric single‐index model is not correctly fitted for the data, we must apply some other more flexible regression models; A single index model (SIM) summarizes the effects of the explanatory vari- ables X1 the intercept of the index and the location parameter of the link function: G. One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) is the choice of pilot estimators and complexity Statistical inference for the index parameter in single-index models☆ linear method, we extend the generalized likelihood ratio test to the single-index model. We derive a new model selection criterion for single-index models,. C approach to model selection across both parametric and nonparametric functions .
The link function f is considered an infinite-dimensional nuisance parameter. Such models arise in Friedman and. Stuetzle's (1981) projection pursuit regression,
16 Jan 2013 In this talk, we consider the semi-parametric model class of single and multiple index models. Here, the regression function is assumed to be a compared with a parametric model, and it avoids the curse of dimensionality because the single- index reduces the dimensionality of a standard variable vector
Single index models The single index model is de–ned as: y = g(Xβ)+ε Advantage 1: generalizes the linear regression model (which assumes g() is linear) Advantage 2: the curse of dimensionality is avoided as there is only one nonparametric dimension Vincenzo Verardi Semiparametric regression 12/09/2013 3 / 66
Implement CER Model & Single Index Model with Point Estimation & Interval Estimation. Use Classical method & Non-parametric Bootstrap (Percentile method, Let (X,Y) be a random pair taking values in Rp × R. In the so-called single-index model, one has Y = f*(θ*TX)+W, where f* is an unknown univariate measurable
A single index model (SIM) summarizes the effects of the explanatory vari- ables X1 the intercept of the index and the location parameter of the link function: G. One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) is the choice of pilot estimators and complexity