SIMULTANEOUS CONFIDENCE BANDS FOR LINEAR-REGRESSION AND SMOOTHING

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.