Exponential inequalities in linear calibration problem

Zerouati Halima and Dahmani Abdelnasser

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 18, 5251-5262

Abstract: Calibration, also called inverse regression, is a classical problem which appears often in a regression setup under fixed design. The aim of this article is to propose a stochastic method which gives an estimated solution for a linear calibration problem. We establish exponential inequalities of Bernstein–Frechet type for the probability of the distance between the approximate solutions and the exact one. Furthermore, we build a confidence domain for the so-mentioned exact solution. To check the validity of our results, a numerical example is proposed.

Date: 2016
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DOI: 10.1080/03610926.2014.941497

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