Master of Science / Department of Statistics / Weixin Yao / In the fitting of mixtures of linear regression models, the normal assumption has been traditionally used
for the error term and then the regression parameters are estimated by the maximum likelihood estimate
(MLE) using the EM algorithm. Under the normal assumption, the M step of the EM algorithm uses
a weighted least squares estimate (LSE) for the regression parameters. It is well known that the LSE is
sensitive to outliers or heavy tailed error distributions. In this report, we propose a robust mixture of linear
regression model, which replaces the least square criterion with some robust criteria in the M step of the
EM algorithm. In addition, we will use a simulation study to demonstrate how sensitive the traditional
mixture regression estimation method is to outliers or heavy tailed error distributions and compare it with
our proposed robust mixture regression estimation method. Based on our empirical studies, our proposed
robust estimation method works comparably to the traditional estimation method when there are no outliers
and the error is normally distributed but is much better if there are outliers or the error has heavy tails
(such as t-distribution). A real data set application is also provided to illustrate the effectiveness of our
proposed methodology.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/4613 |
| Date | January 1900 |
| Creators | Bai, Xiuqin |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Report |
Page generated in 0.0017 seconds