Fan Jianqing, Wu Yichao, Feng Yang
Princeton University.
Ann Stat. 2009 Dec;37(6B):4153-4183. doi: 10.1214/09-AOS713.
Generalized linear models and quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification and the resulting model is completely determined by the data themselves. However nonparametric estimation schemes generally have a slower convergence rate such as the local polynomial smoothing estimation of nonparametric generalized linear models studied in Fan, Heckman and Wand (1995). In this work, we propose two parametrically guided nonparametric estimation schemes by incorporating prior shape information on the link transformation of the response variable's conditional mean in terms of the predictor variable. Asymptotic results and numerical simulations demonstrate the improvement of our new estimation schemes over the original nonparametric counterpart.
广义线性模型和拟似然方法扩展了普通回归模型，以适应响应变量更一般的条件分布。非参数方法不需要明确的参数设定，所得模型完全由数据本身决定。然而，非参数估计方案的收敛速度通常较慢，例如Fan、Heckman和Wand（1995）研究的非参数广义线性模型的局部多项式平滑估计。在这项工作中，我们通过纳入关于响应变量条件均值的链接变换相对于预测变量的先验形状信息，提出了两种参数引导的非参数估计方案。渐近结果和数值模拟表明，我们的新估计方案相对于原始非参数方案有改进。
