A nonparametric calibration analysis. (English) Zbl 0867.62028
Summary: 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 P. Bickel and M. Rosenblatt [ibid. 1, 1071-1095 (1973; Zbl 0275.62033)].
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.
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.
MSC:
| 62G07 | Density estimation |
| 62G35 | Nonparametric robustness |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G15 | Nonparametric tolerance and confidence regions |
Keywords:
invariance principle; nonparametric regression; calibration problems; robust estimation; strong approximations; extreme value theorem; asymptotic simultaneous tolerance regions; nonparametric calibrationCitations:
Zbl 0275.62033References:
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