An Ancillary Paradox in Testing

• Autorzy: He K.
• Języki publikacji: EN

Abstrakty

EN

In multiple linear regression with normally distributed errors, it is shown that a test procedure for a hypothesis about the intercept which is α-admissible when the design matrix is fixed is inadmissible when the design matrix is an ancillary statistic. The result of this paper is a complementary one to Brown's paper [2].

Słowa kluczowe

EN

linear regression; Brown's theory; ancillary paradox

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 1
• Strony: 15--21
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

He K.

• 5600 Fishers Lane, Room 15B-45, DBI/HFD-710, Food and Drug Administration, Rockville, MD 20857, U.S.A.

Bibliografia

• [1] L. D. Brown, On the admissibility of invariant estimators of one or more location parameters, Ann. Math. Statist. 37 (1966), pp. 1087-1135.
• [2] - An ancillarity paradox which appears in multiple linear regression (with discussion), Ann. Statist. 18 (1990), pp. 471-538.
• [3] R. A. Fisher, The logic of inductive inference (with discussion), J. Roy. Statist. Soc. Ser. A 98 (1935), pp. 39-54.
• [4] K. He, An ancillarity paradox in the estimation of multinomial probabilities, J. Amer. Statist. Assoc. 85 (1990), pp. 824-828.
• [5] - The estimation of stratum means vector with random sample sizes, J. Statist. Plann. Inference 37 (1993), pp. 43-50.
• [6] - On estimating a linear combination of stratum means with random sample sizes, J. Multivariate Analysis 55 (1995), pp. 39-60.
• [7] - On estimating domain totals over a subpopulation, Ann. Inst. Statist. Math. 47 (1995) pp. 637-644.
• [8] - and W. E. Strawderman, Estimation in the elliptically contoured regression with random design, manuscript under review, 1995.
• [9] E. L. Lehmann, Testing Statistical Hypotheses, 2nd edition, Wiley, New York 1986.