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August 1996 A nonparametric calibration analysis
Marie-Anne Gruet
Ann. Statist. 24(4): 1474-1492 (August 1996). DOI: 10.1214/aos/1032298278


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.


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Marie-Anne Gruet. "A nonparametric calibration analysis." Ann. Statist. 24 (4) 1474 - 1492, August 1996.


Published: August 1996
First available in Project Euclid: 17 September 2002

zbMATH: 0867.62028
MathSciNet: MR1416643
Digital Object Identifier: 10.1214/aos/1032298278

Primary: 62G05 , 62G20
Secondary: 62G15 , 62G35

Keywords: Calibration , invariance principle , Nonparametric regression , robust estimation , simultaneous tolerance intervals

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 4 • August 1996
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