Asymptotic Theory of Overparameterized Structural Models
研究了过参数化结构模型，其中参数向量不可识别、信息矩阵奇异，证明了最小差异函数检验统计量在广泛差异函数类下几乎处处渐近服从卡方分布，并探讨了估计量的渐近分布性质，以因子分析模型为例。
Abstract A theory of overparameterized structural models is presented. In such a model some “redundant” parameters are involved; the parameter vector is not identified, and the information matrix is not nonsingular. The minimum discrepancy function (MDF) test statistic is shown to have an asymptotic chi-squared distribution almost everywhere for a wide class of discrepancy functions. Asymptotic distribution properties of the MDF estimators are investigated. The factor analysis model is discussed as an example.