The Annals of Statistics

Sequential methods for design-adaptive estimation of discontinuities in regression curves and surfaces

Peter Hall and Ilya Molchanov

Full-text: Open access

Abstract

In fault-line estimation in spatial problems it is sometimes possible to choose design points sequentially, by working one's way gradually through the "response plane," rather than distributing design points across the plane prior to conducting statistical analysis. For example, when estimating a change line in the concentration of resources on or under the sea bed, individual measurements can be particularly expensive to make. In such cases, sequential, design-adaptive methods are attractive. Appropriate methodology is largely lacking, however, and the potential advantages of taking a sequential approach are unclear. In the present paper we address both these problems. We suggest a methodology based on "sequential refinement with reassessment" that relies upon assessing the correctness of each sequential result, and reappraising previous results if significance tests show that there is reason for concern. We focus part of our attention on univariate problems, and we show how methods for the spatial case can be constructed from univariate ones.

Article information

Source
Ann. Statist., Volume 31, Number 3 (2003), 921-941.

Dates
First available in Project Euclid: 25 June 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1056562467

Digital Object Identifier
doi:10.1214/aos/1056562467

Mathematical Reviews number (MathSciNet)
MR1994735

Zentralblatt MATH identifier
1028.62069

Subjects
Primary: 62L12: Sequential estimation
Secondary: 62G20: Asymptotic properties 62H11: Directional data; spatial statistics

Keywords
Changepoint fault line hypothesis test nonparametric estimation recursive search methods spatial statistics

Citation

Hall, Peter; Molchanov, Ilya. Sequential methods for design-adaptive estimation of discontinuities in regression curves and surfaces. Ann. Statist. 31 (2003), no. 3, 921--941. doi:10.1214/aos/1056562467. https://projecteuclid.org/euclid.aos/1056562467


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