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 F 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.

中文翻译：

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非线性变系数模型及其在光合作用研究中的应用。


在对影响自然生态系统光合活动水平的因素的研究的推动下，我们提出了非线性变系数模型，其中预测变量和响应变量之间的关系允许是非线性的。针对非线性变化系数模型开发了一步局部线性估计器，并建立了它们的渐近正态性，从而产生了系数函数的逐点渐近置信带。对于不同系数函数允许不同平滑度的情况，还提出了两步局部线性估计器；引导置信区间用于基于两步估计器的推理。我们进一步提出了广义 F 检验来研究系数函数是否随协变量变化。我们通过对生态数据集的应用来说明所提出的方法，并通过蒙特卡罗模拟研究来研究有限样本性能。