生长曲线模型的分位数回归

生长曲线模型有着广泛的应用, 在经济学、生物学、医学等各个领域的研究都起着重要的作用. 已有文献关于生长曲线模型参数矩阵的估计基本上是使用最小二乘方法或极大似然方法. 使用最小二乘方法, 当误差项服从偏峰分布、厚尾分布、或者存在异常点时, 得出的估计不是有效的; 使用极大似然方法, 要求分布已知, 实际使用时很难满足这一点. 分位数回归能弥补如上这些缺陷, 所得估计具有很好的稳健性. 本文使用分位数回归方法给出生长曲线模型参数矩阵的估计, 及其渐近正态性.

Quantile Regression for Growth Curve Model

Growth curve model has broad application background, and plays an important role in some fields such as economics, biology, medical research. Many of existing estimation of its parameter matrix have been obtained based on the least squares method or maximum likelihood method. When distribution of the error term is partial peak, or heavy tail, or there exist outliers, estimation obtained by least square method will be invalid. The distribution of the error must be known in maximum likelihood estimation, which is often not satisfied. Quantile regression method can compensate for these defects and the estimation has good robustness. In this paper, quantile regression is used to give the estimation of growth curve model, and its asymptotic normality.