Print Email Facebook Twitter Nonparametric confidence intervals for monotone functions Title Nonparametric confidence intervals for monotone functions Author Groeneboom, P. Jongbloed, G. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2015-08-03 Abstract We study nonparametric isotonic confidence intervals for monotone functions. In [Ann. Statist. 29 (2001) 1699–1731], pointwise confidence intervals, based on likelihood ratio tests using the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the treatment of other models with monotone functions, and demonstrate our method with a new proof of the results of Banerjee–Wellner [Ann. Statist. 29 (2001) 1699–1731] and also by constructing confidence intervals for monotone densities, for which a theory remained be developed. For the latter model we prove that the limit distribution of the LR test under the null hypothesis is the same as in the current status model.We compare the confidence intervals, so obtained, with confidence intervals using the smoothed maximum likelihood estimator (SMLE), using bootstrap methods. The “Lagrange-modified” cusum diagrams, developed here, are an essential tool both for the computation of the restricted MLEs and for the development of the theory for the confidence intervals, based on the LR tests. To reference this document use: http://resolver.tudelft.nl/uuid:b581d855-060d-42e8-a020-fcb8c9d010e8 Publisher Institute of Mathematical Statistics ISSN 0090-5364 Source https://doi.org/10.1214/15-AOS1335 Source Annals of Statistics, 43 (5), 2015 Part of collection Institutional Repository Document type journal article Rights (c) 2015 Institute of Mathematical Statistics Files PDF euclid.aos.1438606852.pdf 598.77 KB Close viewer /islandora/object/uuid:b581d855-060d-42e8-a020-fcb8c9d010e8/datastream/OBJ/view