Kürüm Esra, Li Runze, Wang Yang, SEntürk Damla
Department of Statistics, Istanbul Medeniyet University, Istanbul, Turkey. (
Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA 16802-2111, USA (
J Agric Biol Environ Stat. 2014 Mar 1;19(1):57-81. doi: 10.1007/s13253-013-0157-7.
Motivated by a study on factors affecting the level of photosynthetic activity in a natural ecosystem, we propose nonlinear varying coefficient models, in which the relationship between the predictors and the response variable is allowed to be nonlinear. One-step local linear estimators are developed for the nonlinear varying coefficient models and their asymptotic normality is established leading to point-wise asymptotic confidence bands for the coefficient functions. Two-step local linear estimators are also proposed for cases where the varying coefficient functions admit different degrees of smoothness; bootstrap confidence intervals are utilized for inference based on the two-step estimators. We further propose a generalized test to study whether the coefficient functions vary over a covariate. We illustrate the proposed methodology via an application to an ecology data set and study the finite sample performance by Monte Carlo simulation studies.
受一项关于影响自然生态系统中光合活动水平因素的研究启发，我们提出了非线性变系数模型，其中预测变量与响应变量之间的关系可以是非线性的。针对非线性变系数模型开发了一步局部线性估计量，并建立了它们的渐近正态性，从而得到系数函数的逐点渐近置信带。对于变系数函数具有不同平滑度的情况，还提出了两步局部线性估计量；基于两步估计量进行推断时使用自助置信区间。我们进一步提出了一种广义检验，以研究系数函数是否随协变量变化。我们通过将所提出的方法应用于一个生态学数据集进行说明，并通过蒙特卡罗模拟研究来考察有限样本性能。
