The Annals of Statistics

A nonparametric calibration analysis

Marie-Anne Gruet

Full-text: Open access

Abstract

In this paper we discuss a new approach to solve calibration problems in a nonparametric setting. This approach is appealing because it yields estimates of the required quantities directly. The method combines kernel and robust estimation techniques. It relies on strong approximations of the estimating process and the extreme value theorem of Bickel and Rosenblatt. Using these results, we first obtain robust pointwise estimates of the parameters of interest. Second, we set up asymptotic simultaneous tolerance regions for many unknown values of the quantity to be calibrated. The technique is illustrated on a radiocarbon dating problem. The nonparametric calibration procedure proves to be of practical, as well as theoretical interest; moreover, it is quick and simple to implement.

Article information

Source
Ann. Statist., Volume 24, Number 4 (1996), 1474-1492.

Dates
First available in Project Euclid: 17 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032298278

Digital Object Identifier
doi:10.1214/aos/1032298278

Mathematical Reviews number (MathSciNet)
MR1416643

Zentralblatt MATH identifier
0867.62028

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62G15: Tolerance and confidence regions 62G35: Robustness

Keywords
Calibration invariance principle nonparametric regression robust estimation simultaneous tolerance intervals

Citation

Gruet, Marie-Anne. A nonparametric calibration analysis. Ann. Statist. 24 (1996), no. 4, 1474--1492. doi:10.1214/aos/1032298278. https://projecteuclid.org/euclid.aos/1032298278


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