标题： 局部拟似然与参数引导 显示英文标题

标题： Local quasi-likelihood with a parametric guide

摘要： 广义线性模型和拟似然法将普通回归模型推广到能够容纳更一般的响应变量条件分布的情形。非参数方法不需要明确的参数设定，所得到的模型完全由数据本身决定。然而，非参数估计方案通常具有较慢的收敛速度，例如，Fan、Heckman 和 Wand [J. Amer. Statist. Assoc. 90 (1995) 141--150] 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，我们提出了一类参数引导的非参数估计方案。这种方法结合了参数方法和非参数方法的优点，并使我们能够引入先验知识。渐近结果和数值模拟表明，我们的新估计方案优于原始的非参数方法。 显示英文摘要

摘要： Generalized linear models and the 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 [J. Amer. Statist. Assoc. 90 (1995) 141--150]. In this work, we propose a unified family of parametrically-guided nonparametric estimation schemes. This combines the merits of both parametric and nonparametric approaches and enables us to incorporate prior knowledge. Asymptotic results and numerical simulations demonstrate the improvement of our new estimation schemes over the original nonparametric counterpart.