Comparison of Some Suggested Estimators Based on Differencing Technique in the Partial Linear Model Using Simulation

Saja Mohammad Hussein

doi:10.21123/bsj.2019.16.4.0918

Abstract

In this paper new methods were presented based on technique of differences which is the difference- based modified jackknifed generalized ridge regression estimator(DMJGR) and difference-based generalized jackknifed ridge regression estimator(DGJR), in estimating the parameters of linear part of the partially linear model. As for the nonlinear part represented by the nonparametric function, it was estimated using Nadaraya Watson smoother. The partially linear model was compared using these proposed methods with other estimators based on differencing technique through the MSE comparison criterion in simulation study.

Highlights

For the following partially linear model: yi xi f i,i 1,2,..., n ...(1)The partially linear model has parametric and nonparametric components; this model is more flexible than the linear model
In this paper when ridge parameter (k) is variable for the diameter elements of the information matrix ( X~' X~), by applying differences technique In the same way that others(14,20,15,24,10) have applied the technique of differences to the model (1) to estimate the linear regression coefficients vector,we propose a new estimator by replace theGRR in (24) by the biasedDGRR,we get the difference-based modified jackknifed generalized ridge regression estimator(DMJGR):
2-When the sample size is n = 100 we found from Table (4) that the partially linear models when using the two proposed estimators (DMJGR)and (DGJR) when the third-order differences coefficients are used and 2 0.1, 0.8, 0.95, were in the last two positions, while the partially linear models with the estimators (DAUGRR) and (DGRR) alternated over the first two positions

Summary

Introduction

For the following partially linear model: yi xi f (ti ) i ,i 1,2,..., n ...(1). A set of differences-based estimators were presented and was suggested difference-based modified jackknifed ordinary ridge estimator(15) for estimating the parametric component of semiparametric regression model The achievement of this estimate was compared with differencebased estimator and difference- based ridge estimator by the criterions MSE and a BIAS. In this paper when ridge parameter (k) is variable for the diameter elements of the information matrix ( X~' X~) , by applying differences technique In the same way that others(14,20,15,24,10) have applied the technique of differences to the model (1) to estimate the linear regression coefficients vector ,we propose a new estimator by replace the ˆGRR in (24) by the biased ˆDGRR ,we get the difference-based modified jackknifed generalized ridge regression estimator(DMJGR):. Tables (2,3) that the partially linear models with proposed estimators (DMJGR)and (DGJR) came in last positions, where (DGRR) and (DAUGRR) in first and second positions respectively when used fourth-order and fifth –order differencing coefficients except that the partially linear model when used (DAUGRR) estimator came first and followed by estimator(DGRR) at a fifth -order differencing coefficients and 2 0.9

HK S1 S2

Conclusion