生长曲线模型的惩罚最小二乘估计

Penalized Least Squares Estimation of Growth Curve Model

主要考虑了生长曲线模型中的参数矩阵的估计.首先基于Potthoff-Roy变换后的生长曲线模型,采用不同的惩罚函数:Hard Thresholding函数,LASSO,ENET,改进LASSO,SACD给出了参数矩阵的惩罚最小二乘估计.接着对不做变换的生长曲线模型,直接定义其惩罚最小二乘估计,基于Nelder-Mead法给出了估计的数值解算法.最后对提出的参数估计方法进行了数据模拟.结果表明自适应LASSO在估计方面效果比较好.

This paper studied the estimation of parameter matrix in the growth curve model.Based on the Potthoff-Roy transform of the growth curve model,and by using different penalty functions：Hard Thresholding function,LASSO, ENET,LASSO,SACD,the penalized least estimation of parameter matrix was given.Then the penalized least squares estimation was defined directly on the growth curve model.The numerical solution algorithm for the estimation was proposed based on the Nelder-Mead method.Finally,the methods for the parameter estimation were simulated.The results show that the adaptive LASSO is better in the estimation results.