Asymptotic Distribution of Test Statistics in the Analysis of Moment Structures Under Inequality Constraints
研究了当参数向量的总体值位于可行域边界时，矩结构模型拟合优度检验统计量的渐近分布是卡方分布的混合，并讨论了如何计算混合权重。
The analysis of moment structural models has become an important tool of investigation in behavioural, educational and economic studies. The chi-squared large-sample test is routinely employed to assess the goodness of fit of the model considered. However, in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met. Here we consider the case where the population value of the parameter vector is a boundary point of the feasible region. We show that in this case the asymptotic distribution of test statistic is a mixture of chi-squared distributions. The problem of finding the corresponding weights is discussed.