正规化矩阵正定时半参数估计量的统计性质

利用补偿最小二乘原理构造加权惩罚平方和,得到半参数模型中正规化矩阵正定时参数和半参数的估计量.从偶然误差的统计特征出发,详细讨论这种平差方法得到的参数估值的一些统计性质,并对半参数平差与最小二乘法的参数估计值进行比较.理论分析表明,通过选取合适的平滑参数,半参数平差方法优于最小二乘法.另外从数理统计的角度对平滑参数的选取进行分析,得到平滑参数的取值范围,也给出了平滑参数对模型精度的影响.

The Statistical Property of Semiparametric Estimators with Positively Definite Regular Matrix

A method for getting the values of the unknown parameters of the semiparametric model is given under the principle of penalized least squares with a positive definite regular matrix. Based on the statistic characteristic of random errors, the mathematical expectation, variance and mean square error of the parameter estimator getting from this method are discussed in detail. The difference between the parameter values that were given by semiparametric models and by general least squares is compared. It is shown clearly by the theoretical analysis and the simulating computation that the method of semiparametric adjustment is better than that of least squares if the smoothing parameter takes a suitable value. The choice for the reasonable value of the smoothing parameter and (it's) influence on the precision of the mathematic model are described.