Performance Evaluation of Some Estimators of Linear Models with Collinearity and Non–Gaussian Error
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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
Edited Conference Proceedings of the 1st International Conference of the Nigeria Statistical Society (NSS).
Abstract
Among typical challenges in numerous multiple
linear regression models are those of multicollinearity and
non–normal disturbances which have created undesirable
consequences for the ordinary least squares (OLS) estimator
which is the popular and naïve technique for estimating linear
models. Thus, it appears so critical to combine strategies for
estimating regression models in order to muddle through while
these challenges are present. In this study, the strength of some
methods of estimating classical linear regression model in the
presence of multicollinearity and non-normal error structures
were investigated. The conventional Least Squares (LS), Ridge
Regression (RR), Weighted Ridge (WR), Robust M-estimation
(M) and Robust Ridge Regression (RRR) methods taking into
accounts M-estimation procedures were considered in this
study. Results from Monte-Carlo study revealed the
superiority of the RRR estimator over others using Mean
Squared Errors (MSE) of parameter estimates and Absolute
Bias (AB) as assessment criteria among others over various
considerations for the distribution of the disturbance term and
levels of multicollinearity. The study concluded that whenever
linear regression modeling is intended and multicollinearity
among the regressors and non-spherical disturbance structure
on the response variable are suspected in a data set, the RRR
estimator should be adopted in order to ensure optimal
efficiency.
Description
Keywords
Non-normal disturbances,, Collinearity,, Weighted Ridge Regression, Robust M-estimation,, Ridge