Asymptotic covariances for the parameters of biadditive models

Denis, Jean-Baptiste and Gower, John C. (1994). Asymptotic covariances for the parameters of biadditive models. Utilitas Mathematica, 46 pp. 193–205.

URL: http://utilitasmathematica.org/

Abstract

The statistical model for the two-way table with expectation

$Y = \textit{m}11^{\mathit{T}}+a1^{\mathit{T}}+1b^{\mathit{T}}+\sum_{u=1}^{\textit{r}}c_{u}d_{u}^{\mathit{T}}$

is increasingly being used to represent the interaction between genotype and environment in plant-breeding experiments. Proper interpretation of analyses based on this model requires estimates of the standard errors of estimated parameter values. This paper provides the asymptotic variances and covariances of the parameters for this model and for similar models in which one or both of the additive parameters are excluded. It is especially concerned with the technical details of their derivations. The results are given for two equivalent ways of parameterizing the models.

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