Restricted difference-based Liu estimator in partially linear model

Abstract

a b s t r a c tPartially linear model is useful in statistical model as a multivariate nonparametric fitting method. This paper deals with statistical inference for the partially linear model in the presence of multicollinearity. When some additional linear restrictions are assumed to hold, the corresponding restricted difference-based Liu estimator for the parametric component is constructed. The asymptotically properties of the proposed estimators are discussed. Finally, a simulation study is presented to explain the performance of the estimators.

New Restricted Liu Estimator in a Partially Linear Model

“…e statisticians have mainly discussed how to estimate the parametric component of β, and many methods have been proposed to estimate β such as methods by Akdeniz and Duran [1], Akdeniz et al [2], Duran and Akdeniz [3], Akdeniz et al [4], Akdeniz et al [5], Heckman [6], Liang [7], Liu et al [8], Speckman [9], Wu [10,11], Wu and Asar [12], Yatchew [13], Yang et al [14], and Yang and Li [15].…”

Difference-based M-estimator of generalized semiparametric model with NSD errors

“…Duran et al [28] investigated the difference-based ridge and Liu-type estimators in semiparametric regression models. Wu [29] discussed a restricted difference-based Liu estimator in partially linear models. Hu et al [30] presented a difference-based Huber-Dutter (DHD) estimator to obtain the root variance σ and parameter β for a partially linear model.…”

A difference-based approach in the partially linear model with dependent errors

“…Hu et al [ 12 ] used a difference-based Huber Dutter estimator (DHD) to obtain the root variance σ and parametric β for partially linear model. Wu [ 13 ] constructed the restricted difference-based Liu estimator for the parametric component of partially linear model. However, in the majority of the previous work it is assumed that errors are independent.…”