ROBUST ANCOVA: HETEROSCEDASTIC CONFIDENCE INTERVALS THAT HAVE SOME SPECIFIED SIMULTANEOUS PROBABILITY COVERAGE

Rand R. Wilcox

《Journal of Data Science》 15卷2期 (2017/04) Pp. 313-328

https://doi.org/10.6339/JDS.201704_15(2).0008

摘要

The paper deals with robust ANCOVA when there are one or two covariates. Let Mj (Y |X) = β0j + β1j X1 + β2j X2 be some conditional measure of location associated with the random variable Y , given X, where β0j , β1j and β2j are unknown parameters. A basic goal is testing the hypothesis H0: M1(Y |X) = M2(Y |X). A classic ANCOVA method is aimed at addressing this goal, but it is well known that violating the underlying assumptions (normality, parallel regression lines and two types of homoscedasticity) create serious practical concerns. Methods are available for dealing with heteroscedasticity and non-normality, and there are well-known techniques for controlling the probability of one or more Type I errors. But some practical concerns remain, which are reviewed in the paper. An alternative approach is suggested and found to have a distinct power advantage.

關鍵字

prediction intervals ； heteroscedasticity ； robust regression ； analysis of covariance