缺损数据下CM算法的改进

Improvement of CM algorithm for missing data problems

针对CM算法的估计值相对不够精确的问题,给出一种在缺损数据条件下,求分布参数的极大似然估计的迭代算法.算法首先通过CM算法求得不够精确的参数估计值,在所得估计值点处做平行切面.再把此切面方程与原参数估计函数方程联立,求相交曲线.在所求得的相交曲线处任取一点作为新的CM算法迭代初始值,重新进行迭代计算,进而得到较为精确估计值.在这个估计值点处,再做平行平面并进行判断直到所得估计值所在平面与原参数估计函数交点只有一个时停止.通过实例分析,用改进的算法所得估计更加精确,更加简单实用.

The first step θ^∧0 is arbitrarily selected in the CM （cyclic-maximization） algorithm, and this makes the estimation error of the estimated value relatively large. Considering the shortcomings of CM algorithm, this paper presented an iterative algorithm for maximum likelihood estimation of distribution parameters under the condition of missing data. Firstly the inaccurate parameter estimated by CM algorithm and algorithm, and a parallel plane in the obtained estimates points was built. The intersection curve was obtained by putting the plane equation with the original equations of parameters estimation function. Taking a point in the intersection curve as a new CM algorithm iterative initial value, a new iterative calculation was carried out, and then an accurate estimate was obtained. At this estimated point, redoing the parallel plane and judgment until the intersection point between estimated with the original parameter estimation function is only one. Through the case analysis, the estimation results with the improved algorithm will be more accurate, more simple and practical.