The Annals of Statistics

A nonparametric calibration analysis

Marie-Anne Gruet

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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

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

First available in Project Euclid: 17 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Calibration invariance principle nonparametric regression robust estimation simultaneous tolerance intervals


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

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