Bivariate splines for spatial functional regression models
Bivariate splines for spatial functional regression models
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DOI：
10.1080/10485250903323180
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发表时间：
2010-01-01
影响因子：
1.2
通讯作者：
Lai, Ming-Jun
中科院分区：
文献类型：
--
作者：
Guillas, Serge;Lai, Ming-Jun
本文考虑了解释变量为随机曲面，响应为真实的随机变量的泛函线性回归模型，在各种情况下，解释变量和噪声都可以是无界的和相关的。三角剖分上的二元样条表示随机表面。我们使用这种表示来构造具有惩罚项的回归函数的最小二乘估计。在样本中的回归量跨越足够大的函数空间的假设下，二元样条逼近性质产生估计的相合性。仿真证明了质量的渐近性质上的一个现实的域。我们还进行了一个应用程序的臭氧浓度预测在美国，说明了预测技巧的方法。
We consider the functional linear regression model where the explanatory variable is a random surface and the response is a real random variable, in various situations where both the explanatory variable and the noise can be unbounded and dependent. Bivariate splines over triangulations represent the random surfaces. We use this representation to construct least squares estimators of the regression function with a penalisation term. Under the assumptions that the regressors in the sample span a large enough space of functions, bivariate splines approximation properties yield the consistency of the estimators. Simulations demonstrate the quality of the asymptotic properties on a realistic domain. We also carry out an application to ozone concentration forecasting over the USA that illustrates the predictive skills of the method.