Aydın Erar

A simulation study on classic and robust variable selection in linear regression

In linear regression analysis, outliers often have large influence in the variable selection process. The aim of this study is to select the subsets of independent variables, which explain dependent variables in the presence of outliers and possible departures from the normality assumption of the error distribution in robust regression analysis. We compared robust and classical variable selection. Here, as a classics selection criteria we used Cp, AICC and AICF which we proposed. Besides we used Andrews, Huber and Hampel M-estimators in computing of the robust variable selection criteria.

Polynomial tapered two-stage least squares method in nonlinear regression

Nonlinear models play an important role in various scientific disciplines and engineering. The parameter estimation of these models should be efficient to make better decisions. Ordinary least squares (OLS) method is used for estimating the parameters of nonlinear regression models when all regression assumptions are satisfied. If there is a problem with these assumptions, OLS fails to give efficient results. This paper examines the efficiency of parameter estimation under the problem of autocorrelated errors. Some methods have been proposed in order to overcome the problem and obtain efficient parameter estimates especially for autoregressive (AR) processes. One of the most commonly used method is two-stage least squares (2SLS). This method is based on generalized least squares. In this paper, a novel approach is proposed for 2SLS method by evaluating a polynomial tapering procedure on autocorrelated errors. This new method is called tapered two-stage least squares (T2SLS). The finite sample properties and improvements of T2SLS are explored by means of some real life examples and a Monte Carlo simulation study. Both numerical and experimental results reveal that T2SLS can give more efficient parameter estimates especially in small samples under the autocorrelation problem when compared to OLS and 2SLS.

An Alternative Method Correcting BDR Type of Heteroscedasticity by the Weighting Re-estimated Absolute Residuals

ABSTRACT The aim of this paper is to introduce a new method which corrects residual variances for the butterfly distributed residuals (BDR). Distribution theory, confidence intervals, and tests of hypotheses are valid and meaningful only if the standard regression assumptions are satisfied. Heteroskedasticity is one of the violations of these assumptions and BDR is another type of heteroskedasticity. This study reveals an alternative approach to correct the BDR type of heteroskedasticity by the weighting re-estimated absolute residuals (WRAR). After giving brief information about heteroskedasticity and BDR type of heteroskedasticity, WRAR is introduced. WRAR and the usual variance stabilizing techniques are compared on multiple and simple regression models.