Abstract
This paper proposes adapting the semiparametric partial model (PLM) by mixing different estimation procedures defined under different conditions. Choosing an estimation method of PLM, from several estimation methods, is an important issue, which depends on the performance of the method and the properties of the resulting estimators. Practically, it is difficult to assign the conditions which give the best estimation procedure for the data at hand, so adaptive procedure is needed. Kernel smoothing, spline smoothing, and difference based methods are different estimation procedures used to estimate the partially linear model. Some of these methods will be used in adapting the PLM by mixing. The adapted proposed estimator is found to be a square root-consistent and has asymptotic normal distribution for the parametric component of the model. Simulation studies with different settings, and real data are used to evaluate the proposed adaptive estimator. Correlated and non-correlated regressors are used for the parametric components of the semiparametric partial model (PLM). Best results are obtained in the case of correlated regressors than in the non-correlated ones. The proposed adaptive estimator is compared to the candidate model estimators used in mixing. Best results are obtained in the form of less risk error and less convergence rate for the proposed adaptive partial linear model (PLM).
Highlights
Different methods are used for combining regression models
This paper proposes adapting the partial linear model (PLM) by combining different estimation procedures and the resulting regression model called adaptive partial linear model (APLM)
The proposed APLM algorithm for mixing the three procedures is determined as follows: 1. The used data are splitted into two equal sections, the first section is used for estimation and the second is used for prediction evaluation
Summary
Different methods are used for combining regression models. Most combinations are imposed to parametric or nonparametric candidate models (see for example, [14, 29, 30, 3, 20, 31]). Yang (2001) proposed a method for combining nonparametric regression procedures, this method is called adaptive regression procedures by mixing (ARM). This method worked under Gaussian errors, and can be used where there are multiple candidate error distributions. Linear models have been first considered by these researchers [7, 4, 23, 27]. A partial linear model (PLM) is a semiparametric regression model which contains two components, one is parametric and the other is nonparametric. Parametric estimation methods are used to estimate the parametric component, and the nonparametric estimation methods are used to estimate the nonparametric one [9, 19]
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