A spectral form of the dispersion model in designs with arbitrarily unequal block sizes

Zhiyi Zhang

Statistics & Probability Letters, 1992, vol. 15, issue 4, 313-319

Abstract: Under a usual additive mixed model, a spectral decomposition is given to each observed vector Y from a class of block designs with arbitrarily unequal block sizes. As a result, an analysis of variance, in the sense defined by Graybill and Hultquist (1961) and Speed (1987), exist for such a design. The intrablock anova is discussed. Furthermore based on the dispersion structure, it is seen that the unbalancedness forces some useful information beyond the intrablock analysis, and even interblock comparisons. Let a group be a set of observations from the blocks of same sizes, a further decomposition of the spectral form provides an intergroup comparison which completes the anova of such designs.

Keywords: Anova; mixed; model; unequal; block; sizes; spectal; form; of; a; dispersion; matrix; stratum; variances; intrablock; interblock; intergroup. (search for similar items in EconPapers)
Date: 1992
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