【摘要】 研究了一般增长曲线模型中线性可预测变量的最优预测问题,分别在μ(ΔL) μ(Z′)和μ(VK′) μ(X)的条件下得到了线性可预测变量的最优线性无偏预测.特别地,考虑了一类特殊的预测函数:Φ 线性预测函数,得到了Φ 可预测变量的最优Φ 线性无偏预测.结果表明,任意两个最优线性无偏预测以及最优Φ 线性无偏预测都以概率为1相等,从而将这方面的结果推广到一般增长曲线模型.更多还原

【Abstract】 We investigated the problem of optimal predicti on for linear predictabl e variable in the general growth curve model. If μ(ΔL)μ(Z′)orμ(VK′) μ(X) holds, the optimum-linear-unbiased predictors of linear predi ctable variable are obtained respectively. Spe cially, we considered a class of special prediction function: Φ-li near prediction function, and obtained the optimum Φ-linear unbiased predictors o f Φ-linear pred ictable variable. The results show that any optimum-linear-unbiased predictor and opt imum-linear-unbiased predictor are unique with probability one, thus extendin g the results of optimal prediction to the general growth curve model.更多还原