SIMULTANEOUS CONFIDENCE BANDS FOR LINEAR-REGRESSION AND SMOOTHING
SIMULTANEOUS CONFIDENCE BANDS FOR LINEAR-REGRESSION AND SMOOTHING
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DOI：
10.1214/aos/1176325631
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发表时间：
1994-09-01
影响因子：
4.5
通讯作者：
LOADER, CR
中科院分区：
文献类型：
--
作者：
SUN, JY;LOADER, CR
假设Y-i = f(x(i)) + epsilon(i), i = 1，…，n。我们希望为{f(x)， x是x的一个元素}找到近似的1- α同时置信区域。我们的区域将围绕参数或非参数f(x)的上限(x)的线性估计（$）。在这个问题上已有大量的工作。通常对x的某些或全部维数、可考虑的函数类f、cap f上的线性估计类（$）和区域x都有实质性的限制。我们提出的方法是对管式公式的近似，可用于多维x和广泛的线性估计类。通过考虑偏置的影响，我们可以放宽对所考虑的函数f类的假设。仿真和数值计算说明了该方法的性能。
Suppose we observe Y-i = f(x(i)) + epsilon(i), i = 1,...,n. We wish to find approximate 1-alpha simultaneous confidence regions for {f(x), x is an element of x}. Our regions will he centered around linear estimates ($) over cap(x) of parametric or nonparametric f(x). There is a large amount of previous work on this subject. Substantial restrictions have been usually placed on some or all of the dimensionality of x, the class of functions f that can be considered, the class of linear estimates ($) over cap f and the region x. The method we present is an approximation to the tube formula and can be used for multidimensional x and a wide class of linear estimates. By considering the effect of bias we are able to relax assumptions on the class of functions f which are considered. Simulations and numerical computations are used to illustrate the performance.