Inference under Heteroscedasticity of Unknown Form Using an Adaptive Estimator

• Published in: Communications in statistics. Theory and methods 2011-12, Vol.40 (24), p.4431-4457
• Main Authors: Ahmed, Munir, Aslam, Muhammad, Pasha, G. R.
• Format: Article
• Language: English
• Subjects: Adaptive estimator; Estimated weighted least squares; Estimators; Exact sciences and technology; General topics; Global analysis, analysis on manifolds; HCCME; Heteroscedasticity-consistent interval estimator; Kernel weighted least squares; Least squares method; Linear inference, regression; Mathematical analysis; Mathematical models; Mathematics; Null rejection rate; Parametric inference; Probability and statistics; Regression; Samples; Sciences and techniques of general use; Size distortion; Statistical analysis; Statistics; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2010.513793

The heteroscedasticity consistent covariance matrix estimators are commonly used for the testing of regression coefficients when error terms of regression model are heteroscedastic. These estimators are based on the residuals obtained from the method of ordinary least squares and this method yields inefficient estimators in the presence of heteroscedasticity. It is usual practice to use estimated weighted least squares method or some adaptive methods to find efficient estimates of the regression parameters when the form of heteroscedasticity is unknown. But HCCM estimators are seldom derived from such efficient estimators for testing purposes in the available literature. The current article addresses the same concern and presents the weighted versions of HCCM estimators. Our numerical work uncovers the performance of these estimators and their finite sample properties in terms of interval estimation and null rejection rate.