Xycoon logo
Linear Regression
Home    Site Map    Site Search    Xycoon College    Free Online Software    
horizontal divider
vertical whitespace

Online Econometrics Textbook - Regression Extensions - Assumption Violations of Linear Regression

[Home] [Up] [SUR] [Simultaneity] [Multicollinearity] [Restricted LS] [Distributed Lags] [Assumption Violations]

[Heteroskedasticity] [Autocorrelation] [Nonlinearities] [Nonnormality] [Misspecification]

In the previous chapter we have discussed linear regression analysis under some specific assumptions. In this section we will investigate what can be done in case the assumptions of OLS or MLE are violated.

Suppose that

Online Econometrics Textbook - Regression Extensions - Assumption Violations of Linear Regression

(III.I-1)

with

(III.I-2)

(III.I-3)

which implies that the parameters are unbiased but inefficient.

A solution to this problem might be found by using Generalized Least Squares (GLS).

We know that

(III.I-4)

and therefore

(III.I-5)

In a first step we use the matrix P to transform y, X, and e as follows

(III.I-6)

It then follows

(III.I-7)

The unbiased GLS estimator can be written as

(III.I-8)

with

(III.I-9)

and an unbiased estimator for the variance

(III.I-10)

(III.I-11)

Suppose that

(III.I-12)

The log likelihood function is now equal to

(III.I-13)

Hence the GMLE estimator is

(III.I-14)

which is BLUE and

(III.I-15)

which is obviously biased. This problem can be solved by replacing T by T - K (cfr. eq. (III.I-10)).

vertical whitespace




Home
Up
SUR
Simultaneity
Multicollinearity
Restricted LS
Distributed Lags
Assumption Violations
Heteroskedasticity
Autocorrelation
Nonlinearities
Nonnormality
Misspecification
horizontal divider
No news at the moment...
horizontal divider

© 2000-2012 All rights reserved. All Photographs (jpg files) are the property of Corel Corporation, Microsoft and their licensors. We acquired a non-transferable license to use these pictures in this website.
The free use of the scientific content in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission.

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically updates the information without notice. However, we make no warranties or representations as to the accuracy or completeness of such information, and it assumes no liability or responsibility for errors or omissions in the content of this web site. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Contributions and Scientific Research: Prof. Dr. E. Borghers, Prof. Dr. P. Wessa
Please, cite this website when used in publications: Xycoon (or Authors), Statistics - Econometrics - Forecasting (Title), Office for Research Development and Education (Publisher), http://www.xycoon.com/ (URL), (access or printout date).

Comments, Feedback, Bugs, Errors | Privacy Policy Web Awards