Guaranteed characterization of exact non-asymptotic confidence regions

Michel Kieffer (1, 2) , Eric Walter (1)

1 L2S - Laboratoire des signaux et systèmes
2 IUF - Institut Universitaire de France

In parameter estimation, it is often desirable to supplement the estimates with an assessment of their quality. A new family of methods proposed by Campi et al. for this purpose is particularly attractive, as it makes it possible to obtain exact, non-asymptotic con dence regions under mild assumptions on the noise distribution. A bottleneck of this approach, however, is the numerical characterization of these con dence regions. So far, it has been carried out by gridding, which provides no guarantee as to its results and is only applicable to low dimensional spaces. This paper shows how interval analysis can contribute to removing this bottleneck.

Domains: Mathematics [math]; Statistics [math.ST]; Statistics [stat]; Statistics Theory [stat.TH]; Computer Science [cs]; Signal and Image Processing; Engineering Sciences [physics]; Signal and Image processing

Michel Kieffer, Eric Walter. Guaranteed characterization of exact non-asymptotic confidence regions. 2013. ⟨hal-00879937⟩