Adaptive varying-coefficient linear models
Adaptive varying-coefficient linear models
复制标题
DOI：
10.1111/1467-9868.00372
复制
发表时间：
2003-01-01
影响因子：
5.8
通讯作者：
Cai, ZW
中科院分区：
文献类型：
--
作者：
Fan, JQ;Yao, QW;Cai, ZW
变系数线性模型源于多元非参数回归、非线性时间序列建模和预测、函数数据分析、纵向数据分析等。常见的做法是假设变化的系数是给定变量（通常称为指数）的函数。为了大幅扩大建模能力，本文探索了一类变系数线性模型，其中指标未知，并被估计为回归量和/或其他变量的线性组合。我们搜索索引，以便派生的变系数模型为底层未知的多维回归函数提供最小二乘近似。该搜索是通过新提出的混合反向拟合算法来实现的。该算法的核心是通过一步法估计指数和通过一维局部线性平滑估计系数函数之间的交替迭代。结合使用 t 统计量和 Akaike 信息准则来选择局部显着变量。我们进一步扩展了具有两个索引的模型的算法。仿真表明，所提出的方法对于复杂的多元非线性结构建模具有相当大的灵活性，并且对于普通现代计算机来说实际上是可行的。通过1925-1994年的加拿大水貂-麝香鼠数据和1974-1983年的英镑-美元汇率进一步说明了这些方法。
Varying-coefficient linear models arise from multivariate nonparametric regression, non-linear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an index. To enlarge the modelling capacity substantially, this paper explores a class of varying-coefficient linear models in which the index is unknown and is estimated as a linear combination of regressors and/or other variables. We search for the index such that the derived varying-coefficient model provides the least squares approximation to the underlying unknown multidimensional regression function. The search is implemented through a newly proposed hybrid backfitting algorithm. The core of the algorithm is the alternating iteration between estimating the index through a one-step scheme and estimating coefficient functions through one-dimensional local linear smoothing. The locally significant variables are selected in terms of a combined use of the t-statistic and the Akaike information criterion. We further extend the algorithm for models with two indices. Simulation shows that the methodology proposed has appreciable flexibility to model complex multivariate nonlinear structure and is practically feasible with average modern computers. The methods are further illustrated through the Canadian mink-muskrat data in 1925-1994 and the pound-dollar exchange rates in 1974-1983.