半参数可加模型的广义Liu估计

Generalized Liu Estimation in Semiparametric Additive Models

作为部分线性模型和可加模型的推广,半参数可加模型在统计建模中应用广泛.考虑这类半参数模型在线性部分自变量存在共线性时的估计问题.基于Profile最小二乘方法,提出了参数分量的广义Profile-Liu估计,并给出了该估计量的偏和方差以及均方误差.最后利用数值模拟验证了所提方法的有效性.

As a useful extension of partially linear models and additive models, semipara-metric additive models is useful in statistical modelling. This paper considers the estimation of this semiparametric model in the presence of multi-collinearity. Based on the profile least-squares approach, the generalized Liu estimator of the parametric component is proposed, and its bias, variance and mean squares errors are provided. Finally, some simulation was conducted to illustrate the performance of the proposed method.