中文摘要：

生长曲线模型是一个典型的多元线性模型,在现代统计学上占有重要地位.文章首先基于Potthoff-Roy变换后的生长曲线模型,采用自适应LASSO为惩罚函数给出了参数矩阵的惩罚最小二乘估计,实现了变量的选择.其次,基于局部渐近二次估计,对生长曲线模型的惩罚最小二乘估计给出了统一的近似估计表达式.接着,讨论了经过Potthoff-Roy变换后模型的惩罚最小二乘估计,证明了自适应LASSO具有Oracle性质.最后对几种变量选择方法进行了数据模拟.结果表明自适应LASSO效果比较好.另外,综合考虑,Potthoff-Roy变换优于拉直变换.

英文摘要：

Growth curve model is a general multivariable linear model.It plays an important role in modern statistics.In this paper,firstly,we define the penalized least squares for growth curve model,after transforming it by the Potthoff-Roy transformation.By using adaptive LASSO we can get corresponding estimation,as well as achieve the variable selection.Then,the penalized least squares estimation of the growth curve model is presented with a unified expression of approximate estimation.In addition,we discuss the properties of the penalized least squares estimations of the growth curve model,which is transformed by Potthoff-Roy transformation,and the properties,which are Oracle properties,are proved in this paper.By using the criteria to measure estimation and variable selection,we compare several penalized least squares estimations and the effect of variable selection of different penalty functions.The result shows that the adaptive LASSO performs better in parameter estimation and variable selection.Besides,we compare different transformations.Results indicate that Potthoff-Roy transformation performs better than matrix stacking transformation when considering variable selection and parameter estimation comprehensively.