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 Keywords: Dimension reduction; parametric single index models; model-adaptation; model check-ing. 1. Introduction Consider the following parametric single-index regression model: Y = g(βT 0 X,θ0)+ϵ, (1) †Address for correspondence: Lixing Zhu, lzhu@hkbu.edu.hk. In the paper, a model adaptation concept in lack‐of‐fit testing is introduced and a dimension reduction model‐adaptive test procedure is proposed for parametric single‐index models. The test behaves like a local smoothing test, as if the model were univariate.
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 are useful and fundamental tools for handling ''curse of dimen- sionality'' problems in nonparametric regression. Along with that, variable
Finally, we develop a lin- ear hypothesis test for the parametric coefficients and a goodness-of-fit test for the nonparametric component, respectively. Monte Carlo Generally used to fit a parametric model in which the partially linear models and single index models The single index model is defined as: B # 2 ,p! " e. Implement CER Model & Single Index Model with Point Estimation & Interval Estimation. Use Classical method & Non-parametric Bootstrap (Percentile method,
The link function f is considered an infinite-dimensional nuisance parameter. Such models arise in Friedman and. Stuetzle's (1981) projection pursuit regression, the commonly-used fully-parametric growth regression models, the single-index model has two advantages: (1) the link function is more flexible; and (2) it allows
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 are useful and fundamental tools for handling ''curse of dimen- sionality'' problems in nonparametric regression. Along with that, variable Most parametric models are single index, including Normal regression, Logit, Probit, Tobit, and Poisson regression. In a semiparametric single index model, the object of interest depends on x through the function g(x0 ) where 2 Rk and g : R ! R are unknown. g is sometimes called a link function. In single index models, there is only one nonparametric dimension. The single index model takes its name from the parametric part of the model ′ which is a scalar single index. The nonparametric part is the unknown function (⋅). Ichimura's method. The single index model method developed by Ichimura (1993) is as follows. When single-index components are nuisance parameters that are plugged into the second step estimation of a –nite dimensional parame-ter of interest, the introduction of single-index restrictions does not improve the convergence rate of the estimated parameter of interest which already achieves the parametric rate of p n: