生长曲线模型下的统一有偏估计

Unified Biased Estimators of Parameters in Growth Curve Models

生长曲线模型有很重要的实际应用背景,针对该模型存在的复共线性问题,本文将统一有偏估计推广到生长曲线模型下,提出多元统一有偏估计。并讨论了它的可容许性,找到了它一致优于最小二乘估计的椭球范围。同样,在实际应用中还会经常遇到带约束的生长曲线模型,针对此时存在着的复共线性问题作了类似的研究,提出了约束多元统一有偏估计。

There is an important practical background for growth-curve models, in view of the model of the multi-collinearity problem, we study the unified biased estimation of growth-curve model, and propose the multivariate unified biased estimation, then we discuss its admissibility, and deduce the elliptical range in which the proposed multivariate unified biased estimation is surely superior to the ordinary least squares estimation. Likewise, we often meet the restricted growth-curve model in practical application of linear models, when the multi-collinearity happens in this model, we propose a new estimation restricted multivariate unified biased estimation.