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Sound Confidence Intervals in the Heteroscedastic Linear Model Through Releveraging
Alan H. Dorfman
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 53, No. 2 (1991), pp. 441-452
Stable URL: http://www.jstor.org/stable/2345754
Page Count: 12
You can always find the topics here!Topics: Leverage, Statistical variance, Least squares, Estimators, Confidence interval, Linear models, Statism, Linear regression, Point estimators, Mathematical constants
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Under heteroscedasticity, ordinary least squares regression can fail to yield adequate inference on parameter coefficients with respect to hypothesis testing or confidence intervals. For example, confidence intervals can have coverage well below that claimed. This is especially the case in small or moderate-sized imbalanced samples and holds even if the ordinary least squares variance estimator is replaced by a robust-against-heteroscedasticity variance estimator. A new simple weighting scheme corrects this problem, although at possibly serious cost in efficiency. Inefficient methods have been rated as useful at the data exploration stage of analysis. The present method is also useful as an adjunct to least squares regression, at the stage of regression diagnostics. As such, it can sometimes replace the need for them altogether.
Journal of the Royal Statistical Society. Series B (Methodological) © 1991 Royal Statistical Society