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作者：Dumbgen, Lutz; Wellner, Jon A.
作者单位：University of Bern
摘要：We introduce new goodness-of-fit tests and corresponding confidence bands for distribution functions. They are inspired by multiscale methods of testing and based on refined laws of the iterated logarithm for the normalized uniform empirical process U-n(t)/root t (1 - t) and its natural limiting process, the normalized Brownian bridge process U(t)/root t (1 - t). The new tests and confidence bands refine the procedures of Berk and Jones (1979) and Owen (1995). Roughly speaking, the high power ...
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作者：Donoho, David; Gavish, Matan; Romanov, Elad
作者单位：Stanford University; Hebrew University of Jerusalem
摘要：We derive a formula for optimal hard thresholding of the singular value decomposition in the presence of correlated additive noise; although it nomi-nally involves unobservables, we show how to apply it even where the noise covariance structure is not a priori known or is not independently estimable. The proposed method, which we call ScreeNOT, is a mathematically solid alternative to Cattell's ever-popular but vague scree plot heuristic from 1966. ScreeNOT has a surprising oracle property: it...
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作者：Steinberger, Lukas; Leeb, Hannes
作者单位：University of Vienna
摘要：We investigate generically applicable and intuitively appealing predic-tion intervals based on k-fold cross-validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training sample (hence, training conditional validity), and show that it is close to the nominal level, in an appropriate sense, provided that the underlying algorithm used for computing point predictions is sufficiently stable when feature-response pairs are omitted. Our...
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作者：Hazimeh, Hussein; Mazumder, Rahul; Radchenko, Peter
作者单位：Alphabet Inc.; Google Incorporated; Massachusetts Institute of Technology (MIT); University of Sydney
摘要：We present a new algorithmic framework for grouped variable selection that is based on discrete mathematical optimization. While there exist several appealing approaches based on convex relaxations and nonconvex heuristics, we focus on optimal solutions for the l(0)-regularized formulation, a problem that is relatively unexplored due to computational challenges. Our methodol-ogy covers both high-dimensional linear regression and nonparametric sparse additive modeling with smooth components. Ou...
