Testing hypotheses in the functional linear model
Testing hypotheses in the functional linear model
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DOI：
10.1111/1467-9469.00329
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发表时间：
2003-03-01
影响因子：
1
通讯作者：
Sarda, P
中科院分区：
文献类型：
--
作者：
Cardot, H;Ferraty, F;Sarda, P
具有标量响应的函数线性模型是一种回归模型，其中预测变量是在某个紧凑的 R 集上定义的随机函数，并且响应是标量。响应被建模为 Y=Psi(X)+epsilon，其中 IF 是在平方可积函数空间上定义的一些线性连续算子。并在 R 中赋值。随机输入 Xi 与噪声无关。在本文中，我们感兴趣的是检验无效假设，即 IF 的无效性仅限于随机变量 X 生成的希尔伯特空间。我们引入了两种基于 (X, 1) 经验互协方差算子范数的检验统计量。第一个检验统计量依赖于 chi(2) 近似，我们在适当的条件下对 X 的协方差算子显示第二个检验统计量的渐近正态性。检验程序可用于检查 X 和 Y 之间的给定关系。该方法通过模拟研究进行说明。
The functional linear model with scalar response is a regression model where the predictor is a random function defined on some compact set of R and the response is scalar. The response is modelled as Y=Psi(X)+epsilon, where IF is some linear continuous operator defined on the space of square integrable functions. and valued in R. The random input Xis independent from the noise's. In this paper, we are interested in testing the null hypothesis of no effect, that is, the nullity of IF restricted to the Hilbert space generated by the random variable X. We introduce two test statistics based on the norm of the empirical cross-covariance operator of (X, 1). The first test statistic relies on a chi(2) approximation and we show the asymptotic normality of the second one under appropriate conditions on the covariance operator of X. The test procedures can be applied to check a given relationship between X and Y. The method is illustrated through a simulation study.