Lineer ve kısmi lineer modeller için cezalı ve cezasız tahmin stratejileri

In this dissertation we obtained pretest ridge regression, shrinkage ridge regression estimators, and compared their performance with penalty estimators in linear and partially linear models. We also investigated asymptotic properties of proposed estimators both analytically and thorough simulation studies. In Chapter 1, we presented preliminary definitions and theorems which are used at the next two chapters. In Chapter 2, we defined pretest ridge regression, shrinkage ridge regression and positive shrinkage ridge regression estimators for a multiple linear regression model, and compared their performance with some penalty estimators which are lasso, adaptive lasso and SCAD. Monte Carlo studies were conducted to compare the estimators in two situations: when p < n and when p > n. Three real data examples for low-dimensional scenario and two real data examples for high-dimensional scenario are presented to illustrate the usefulness of the suggested methods. Finally, we investigated the asymptotic properties of these estimators analytically. In Chapter 3, we defined pretest ridge regression, shrinkage ridge regression and positive shrinkage ridge regression estimators for a partially linear regression model. In this model, the nonparametric function is estimated using the smoothing spline method. We also compared the performance of suggested estimators with some penalty estimators which are lasso, adaptive lasso and SCAD. Monte Carlo studies were conducted to compare the estimators in two situations: when p < n and when p > n. Finally, we investigated the asymptotic properties of these estimators analytically. In Chapter 4, it is given conclusions and future work.