Likelihood-based confidence bands for fault lines in response surfaces |
| |
Authors: | Peter Hall Christian Rau |
| |
Institution: | (1) Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia. This work was supported by a grant on the APAC National Facility under the Merit Allocation Scheme. e-mail: Peter.Hall@anu.edu.au; Christian.Rau@anu.edu.au, AU;(2) CSIRO Mathematical and Information Sciences, Sydney, NSW, Australia, AU |
| |
Abstract: | We consider the problem of constructing asymptotic confidence bands, both pointwise and simultaneous, for a smooth fault
line in a response surface when the design is represented by a point process, either deterministic or stochastic, with intensity
n diverging to infinity. The estimator of the fault line is defined as the ridge line on the likelihood surface which arises
from locally fitting a model that employs a linear approximation to the fault line, to a kernel smooth of the data. The construction
is based on analysis of the limiting behaviour of perpendicular distance from a point on the true fault line to the nearest
point on the ridge. We derive asymptotic properties of bias, and the limiting distribution of stochastic error. This distribution
is given by the location of the maximum of a Gaussian process with quadratic drift. Although the majority of attention is
focused on the regression problem, the limiting distribution is shown to have wider relevance to local-likelihood approaches
to fault line estimation for density or intensity surfaces.
Received: 20 August 2000 / Revised version: 27 September 2001 / Published online: 22 August 2002 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|