数据归并与连续自变量虚拟化

 本文基于数据双侧归并的一般化设定探讨了回归方程中包含归并数据时的参数估计问题。对于某些变量存在数据归并的线性模型，由于样本似然函数非常复杂，普通的一阶优化条件没有解析解，Newton-Raphson迭代也难以收敛。我们基于EM算法来计算参数的ML估计，推导了对应的参数迭代方程，给出了参数的一个闭式解。特别是，当数据双侧归并比例达到100%时，被归并的连续变量退化为虚拟变量的形式，对此，我们建议使用AIC或SC来识别回归方程中的虚拟变量是否为结构变化抑或是变量归并。

Censored Data and Dummy Continuous Regressors

Since the log-likelihood function of sample is very complex for linear models with censored variables, the first order conditions of optimization has not analytical solutions, while Newton-Raphson iteration is too hard to convergent. This paper focuses on the estimation for linear models with two-side censored variables. We calculate the ML estimation via the EM algorithm, and derive its iteration equations, which gives a closed-form solution for parameters. Especially, the continuously censored variables degenerate into dummy variables when the censoring ratio of data arrive 100%, for this situation, we advise to identify whether the dummy variables in regression is structural change or censoring by AIC or SC criteria.