This dissertation is concerned with the estimation of error variances in a non-replicated two-way classification and with inferences based on the estimators so derived. The postulated model used throughout the present work is / y(,ij) = (mu)(,i) + (beta)(,j) + (epsilon)(,ij), / where y(,ij) is the observation in the i('th) row and j('th) column, (mu)(,i) is the parameter representing the mean of the i('th) row, (beta)(,j) is the parameter representing the additional effect of the j('th) column, / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / and the (epsilon)(,ij) are independent, zero-mean, normal variates with / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / A set of unbiased estimates / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / developed in earlier work by Grubbs (J. AMER. STATIST. ASSOC. 43 (1948), 243-264), Ehrenberg (BIOMETRIKA 37 (1950), 347-357) and Russell and Bradley (BIOMETRIKA 45 (1958), 111-129) are considered. / The exact joint density of Q(,1), ..., Q(,r) is obtained for r = 3 and two exact results are derived for testing the null hypothesis, / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / unknown, versus the two specific alternatives, / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / for at least some j, j = 1, 2, 3, and, / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / Source: Dissertation Abstracts International, Volume: 43-07, Section: B, page: 2258. / Thesis (Ph.D.)--The Florida State University, 1982. / These results are consistent with those obtained by Russell and Bradley. / The exact density is derived for the case where r = 4 and n = 4, but no further exact results are obtained. For r = 4 and general n, an approximate test is obtained for testing / unknown, versus / Interesting results regarding the characteristic function of some quadratic forms closely related to Q(,1), ..., Q(,r) are also presented. It is possible to transform the characteristic function in order to obtain the density, and for r = 3 and n = 4, this density is shown to be identical to the density obtained previously for r = 3.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74896 |
| Contributors | BRINDLEY, DENNIS ALFRED., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 94 p. |
| Rights | On campus use only., for at least some j, j = 1, ..., 4. This test is shown to have excellent properties for all n. |
| Relation | Dissertation Abstracts International |
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