Robust estimation for multiple linear regression
Loading...
Date
2008
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
CCSHAU
Abstract
The search for better method of estimation is everlasting.
Assumptions of ordinary least squares provided numerous
opportunities of study when its assumptions are violated in multiple
linear regression. The present study is related to the violation of
normality assumption. Any process which can give relatively better
estimates even after the assumption is violated is a robust estimation
process. Modified maximum likelihood method is one such tool which is
applied in the present study.
Normality assumption of errors is checked with the help of
Q-Q plot. Plots of standardized residuals against each independent
variable were utilized to detect the outlier cases. Deviation from normal
plot gives deviation of each point from normal distribution. Exclusion of
outliers caused considerable changes in the values of R2, adjusted R2
and standard error of estimates.
We considered a distribution which is in reasonable
proximity of error distribution and estimated the unknown parameter
of the distribution. The distribution of errors which violate normality
assumption can broadly be divided into two parts i.e. symmetric and
skewed. Modified maximum likelihood estimates are calculated for a
series of value of unknown parameter and the value having maximum
value of logarithm of likelihood function is selected as the most
plausible value.
In present study, two estimation procedures i.e. MMLE and
OLS were compared in terms of standard error of estimates. MMLE was
found to have lesser standard errors than OLS even when normality
assumption was violated and outliers were present. With the help of
datasets it is concluded that MML estimates are robust.
Description
Keywords
Heterosis, Sowing, Developmental stages, Yields, Planting, Crops, Hybrids, Biological phenomena, Crossing over, Oils