植物反射率的空间函数数据建模
Spatial Functional Data Modeling of Plant Reflectances
摘要：
植物反射光谱--由不同波长的叶子反射的光的轮廓--提供了一个物种在空间位置的光谱特征，从而能够估计植物的功能和分类多样性。我们认为叶光谱作为“响应”空间解释。这些光谱/反射率是响应于环境的波长带上的函数。我们的激励数据收集的几个家庭从南非的开普敦植物区系区（CFR），并导致我们开发丰富的新的空间模型，可以解释谱属内的家庭。单个叶片的波长响应被视为波长的函数，导致功能数据建模。当地的环境特征成为协变量。我们引入波长协变量的相互作用，因为对环境回归的响应可能随波长而变化，方差也可能变化。正式的空间建模，使反射率的预测属在未观察到的位置与已知的环境特征。我们将空间依赖性，波长依赖性和空间波长相互作用（在时空相互作用的精神）。我们实现了样本外验证来选择最佳模型，发现上面列出的模型特征都为函数数据分析提供了信息。然后，我们提供的结果下所选择的模型的解释。
英文摘要：
Plant reflectance spectra - the profile of light reflected by leaves across different wavelengths - supply the spectral signature for a species at a spatial location to enable estimation of functional and taxonomic diversity for plants. We consider leaf spectra as "responses" to be explained spatially. These spectra/reflectances are functions over a wavelength band that respond to the environment. Our motivating data are gathered for several families from the Cape Floristic Region (CFR) in South Africa and lead us to develop rich novel spatial models that can explain spectra for genera within families. Wavelength responses for an individual leaf are viewed as a function of wavelength, leading to functional data modeling. Local environmental features become covariates. We introduce wavelength - covariate interaction since the response to environmental regressors may vary with wavelength, so may variance. Formal spatial modeling enables prediction of reflectances for genera at unobserved locations with known environmental features. We incorporate spatial dependence, wavelength dependence, and space-wavelength interaction (in the spirit of space-time interaction). We implement out-of-sample validation to select a best model, discovering that the model features listed above are all informative for the functional data analysis. We then supply interpretation of the results under the selected model.
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