Approximate Confidence Intervals for Contrasts in the Balanced Three Factor Mixed Model

摘要

When conducting a statistical analysis of data from a designed experiment, an investigator {s often interested in confidence intervals for contrasts of the fixed effect, If the analysis; myolv s a m x d linear model, exact confidence intervals for contrasts of the fixed effects are not always ava.lable. such cases, confidence intervals with approximate coverage probabilities must be useaAS will be shown, tnis promein may be generalized to that of constructing a confidence interval for the parameter μ, where X is a normal random variable with mean μ and variance ∑_(q=1)~Q a_qθ_q, where a1,...a~Q are known constants, U_q=n~pS_1~2/θ_q is a chi-squared random variable with n~q degrees of freedom, for each q=1,...,Q, and X,U_1,...U_Q are mutually independent. In this paper, we consider the case where Q=3 and a_3<0.