TITLE:
Performance of Existing Biased Estimators and the Respective Predictors in a Misspecified Linear Regression Model
AUTHORS:
Manickavasagar Kayanan, Pushpakanthie Wijekoon
KEYWORDS:
Misspecified Regression Model, Generalized Biased Estimator, Generalized Predictor, Mean Square Error Matrix, Scalar Mean Square Error
JOURNAL NAME:
Open Journal of Statistics,
Vol.7 No.5,
October
31,
2017
ABSTRACT: In this paper, the performance of existing biased
estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu
Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component
Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression
model when there exists multicollinearity among explanatory variables. A
generalized form was used to compare these estimators and predictors in the
mean square error sense. Further, theoretical findings were established using
mean square error matrix and scalar mean square error. Finally, a numerical
example and a Monte Carlo simulation study were done to illustrate the
theoretical findings. The simulation study revealed that LE and RE outperform
the other estimators when weak multicollinearity exists, and RE, r-k class
and r-d class estimators outperform the other estimators
when moderated and high multicollinearity exist for certain values of shrinkage
parameters, respectively. The predictors based on the LE and RE are always
superior to the other predictors for certain values of shrinkage parameters.