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作者：Mammen, E; Van de Geer, S
作者单位：Ruprecht Karls University Heidelberg; Leiden University; Leiden University - Excl LUMC
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作者：Dümbgen, L; Spokoiny, VG
作者单位：University of Lubeck; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Suppose that one observes a process Y on the unit interval, where dY(t) = n(1/2)f(t) dt + dW (t) with an unknown function parameter f, given scale parameter n greater than or equal to 1 (sample size) and standard Brownian motion W. We propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity. These tests are asymptotically optimal and adaptive in a certain sense. They are constructed via a new class of multiscale statistics and an extension ...
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作者：Patilea, V
作者单位：Universite de Orleans
摘要：We analyze the asymptotic behavior of maximum likelihood estimators (MLE) in convex dominated models when the true distribution generating the independent data does not necessarily belong to the model. Inspired by the Hellinger distance and its properties, we introduce a family of divergences (contrast functions) which allow a unified treatment of well- and misspecified convex models. Convergence and rates of convergence of the MLE with respect to our divergences are obtained from inequalities...
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作者：Davies, PL; Kovac, A
作者单位：University of Duisburg Essen
摘要：The paper considers the problem of nonparametric regression with emphasis on controlling the number of local extremes. Two methods, the run method and the taut-string multiresolution method, are introduced and analyzed on standard test beds. It is shown that the number and locations of local extreme values are consistently estimated. Rates of convergence are proved for both methods. The run method converges slowly but can withstand blocks as well as a high proportion of isolated outliers. The ...
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作者：Kent, JT; Tyler, DE
作者单位：University of Leeds; Rutgers University System; Rutgers University New Brunswick
摘要：Constrained M-estimates of multivariate location and scatter are found by finding the global minimum of an objective function subject to a constraint. They are related to redescending M-estimates of multivariate location and scatter since any stationary point of the objective function corresponds to such an M-estimate. Unfortunately, even for the population form of the estimator, that is, the constrained dl-functional, the objective function may have multiple stationary points. In this paper, ...
