An evaluation of ridge regression in the presence of multicollinearity

الموضوعات

علوم بحتة وطبيعية

الملخص

In regression, the objective is to explain the variation in one or more response variables, by associating this variation with proportional in one or more explanatory variables. If there is no linear relationship between these explanatory variables, they are said to be orthogonal. If the variables is not orthogonal then several of the explanatory variables will vary in rather similar ways. This problem is called multicollinearity, which is a commonly occurring problem in regression analysis. It is the situation in which two or more explanatory variables are highly (but not perfectly ) correlated to one another, making it difficult to interpret the strength of the effect of each variable. Handling multicollinearity problem in regression analysis is very important because the least squares estimatiors assume that the predictors are not correlated. A number of procedures have been developed for finding biased estimators of regression parameters. Some of these procedures are ridge regression (RR), principal component regression (PCR) and partial least squares regression (PLSR). In this thesis, we consider ridge regression, including the ridge estimator (ordinary and generalized) and their properties. Since the creative work of Hoerl and Kennard ridge regression has proven to be a useful technique to tackle the multicollinearity problem in the linear regression model. Different approaches are investigated with different criteria for estimating the ridge parameter ݇. In this thesis a comparison between well-known approaches for selecting the ridge parameter ݇. Under the normality assumptions, the mean squared error (MSE) criterion is used to examine the performance of these estimators when compared with the ordinary least squared estimator (OLS). The simulation studies and the analysis of real data demonstrate that under certain conditions, at least one of the considered estimators (HKa, KS, HK, FK) have a smaller MSE than the ordinary least squared estimator (OLS), and other approaches.

روابط وملفات

التعريف والنوع

رقم الوثيقة

f6166e12-f969-45f0-b0b4-d7991f87e1b6

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

1696840_1.pdf

بيانات النشر

ترجمة العنوان

حساب ridge estimator في حال وجود مشكلة الارتباط الخطي

ألقاب المؤلفين

[{"name_ar":"خالد صلاح","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"سليمان سمير سليمان الفقيه","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

English

المصدر والدورية

اسم المصدر

An evaluation of ridge regression in the presence of multicollinearity

المحتوى والصفحات

عدد الصفحات

0

إشراف وإعداد

الإشراف

خالد صلاح

الإعداد

سليمان سمير سليمان الفقيه

الاقتباسات الببليوغرافية