More Efficient Tests Robust to Heteroskedasticity of Unknown Form
研究了在异方差形式未知时，基于Cragg估计量的检验在小样本中的有限样本性质，发现该估计量能提供可靠且更有效的检验。
ABSTRACT In the presence of heteroskedasticity of unknown form, the Ordinary Least Squares parameter estimator becomes inefficient, and its covariance matrix estimator inconsistent. Eicker (1963 Eicker , B. ( 1963 ). Limit theorems for regression with unequal and dependant errors . Ann. Math. Statist. 34 : 447 – 456 .[Crossref] , [Google Scholar]) and White (1980 White , H. ( 1980 ). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity . Econometrica 48 : 817 – 838 .[Crossref], [Web of Science ®] , [Google Scholar]) were the first to propose a robust consistent covariance matrix estimator, that permits asymptotically correct inference. This estimator is widely used in practice. Cragg (1983 Cragg , J. G. ( 1983 ). More efficient estimation in the presence of heteroskedasticity of unknown form . Econometrica 51 : 751 – 63 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed a more efficient estimator, but concluded that tests basd on it are unreliable. Thus, this last estimator has not been used in practice. This article is concerned with finite sample properties of tests robust to heteroskedasticity of unknown form. Our results suggest that reliable and more efficient tests can be obtained with the Cragg estimators in small samples.