Nonparametric confidence regions for level sets: Statistical properties and geometry
نویسندگان
چکیده
منابع مشابه
Confidence regions for level sets
This paper discusses a universal approach to the construction of confidence regions for level sets {h(x) ≥ 0} ⊂ Rd of a function h of interest. The proposed construction is based on a plug-in estimate of the level sets using an appropriate estimate �hn of h. The approach provides finite sample upper and lower confidence limits. This leads to generic conditions under which the constructed confid...
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We construct nonparametric confidence sets for regression functions using wavelets. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by showing that a pivot process, constructed from the loss function, converges uniformly to a mean zero Gaussian process. Inverting this pivot yields a confidence set for the wavelet coefficients ...
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In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region An which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in An where simplicity can be defined in term...
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2019
ISSN: 1935-7524
DOI: 10.1214/19-ejs1543