Generalized mixed estimator for nonlinear models: a maximum likelihood approach
研究了在未知参数受随机线性约束时如何估计非线性统计模型，利用混合回归和最大似然法推导了模型系数和设计矩阵未知元素的估计量，并提出了兼容性检验，用模拟和实际营销数据验证了效果。
This paper considers the problem of estimating a nonlinear statistical model subject to stochastic linear constraints among unknown parameters. These constraints represent prior information which originates from a previous estimation of the same model using an alternative database. One feature of this specification allows for the disign matrix of stochastic linear restrictions to be estimated. The mixed regression technique and the maximum likelihood approach are used to derive the estimator for both the model coefficients and the unknown elements of this design matrix. The proposed estimator whose asymptotic properties are studied, contains as a special case the conventional mixed regression estimator based on a fixed design matrix. A new test of compatibility between prior and sample information is also introduced. Thesuggested estimator is tested empirically with both simulated and actual marketing data.