2011 YÜksek lisans tez özetleri

Estımatıon Of The Bıased Parameter In Some Bıased Estımators

In multiple linear regression model, the linear relationship among independent variables is called as multicollinearity. In the present multicolinearity, the ordinary least squares (OLS) estimator is still the best linear unbiased estimator. But, its variance is very large. Therefore, OLS estimator may be far from parameter’s true value. Estimation processes to reduce collinearity effect has led to the emergence of biased estimators. When multicollinearity is present in model, two of biased estimators, which are suggested as alternative to OLS estimator, are Ridge and Liu estimators. But, Ridge and Liu estimators are depended on OLS estimator. Therefore, unstable of OLS estimator effects Ridge and Liu estimators. To overcome this problem, biased estimators which include two biasing parameters are proposed. The aim of this thesis, some biased estimators are suggested are introduction, selection of parameters, and comparison of these estimator with each other in the present of multicollinearity.

The thesis entitled as “Estimation of the Biased Parameter in Some Biased Estimators” consists of six chapter.

In the first chapter, multicollinearity problem is examined as comprehensive. In addition, the determination of multicollinearity, results caused by its, and methods of solution are given.

In the second chapter, definitions and theorems, which are used proof of theorems in later sections, are given.

In the third chapter, in the present multicolinearity in model, Ridge and Liu estimators, which are suggested as alternative to OLS estimator, are introduced and various methods for finding biasing parameters are given. These estimators have comparisoned previously OLS estimator and then each other according to the scalar mean squared error (SMSE) criteria and the matrix mean squared error (MMSE) criteria.

In the fourth chapter, estimators which include as special cases OLS estimator, Ridge estimator and Liu estimator are introduced. Methods for finding biasing parameters of these estimators are given. In addition, estimators which include two biasing parameters are made comparisons with OLS estimator, Ridge estimator, Liu estimator and each other according to the MMSE criterion.

In the fifth chapter, Hald dataset is analysed again. Comparisons which are given theoretical are showed as graphically.

In the last chapter, conclusions are gained are given.