Robustness Properties of the F-Test and Best Linear Unbiased Estimators in Linear Models.
PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS
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Document considers a linear model Y X beta sigma epsilon, Eepsilon O, Eepsilon prime I sub n with beta, sigma unknown. For the problem of testing the linear hypothesis C beta sigma imC prime a subset of imX prime, Ghosh and Sinha 1980 proved that the properties of the usual F-test being LRT and UMPI under a suitable group a transformations remain valid for specific non-normal families. In this paper it is shown that both criterion and inference robustness of the F-test hold under the assumption epsilon about qepsilon prime, q convex and isotonic. This result is similar to a robustness property of Hotellings T squared-test proved by Kariya 1981. Finally it is proved that the Best Linear Unbiased Estimator BLUE of any estimable function beta is more concentrated around C beta than any other unbiased estimator of C beta under the assumption that epsilon is spherically distributed.
- Statistics and Probability