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作者：Omelka, Marek; Gijbels, Irene; Veraverbeke, Noel
作者单位：Charles University Prague; KU Leuven; KU Leuven; Hasselt University
摘要：We reconsider the existing kernel estimators for a copula function. as proposed in Gijbels and Mielniczuk [Comm. Statist. Theory, Methods 19 (1990) 445-464] Fermaman, Radulovic and Wegkamp [Bernoulli 10 (2004) 847-860] and Chen and Huang [Canad. J. Statist. 35 (2007) 265-282]. All of these estimators have as a drawback that they can suffer from a corner bias problem. A way to deal with this is to impose rather stringent conditions on the copula, outruling as such many classical families of cop...
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作者：Spokoiny, Vladimir; Vial, Celine
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
摘要：This paper discusses the problem of adaptive estimation Of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from Lepski [Theory Probab. Appl. 35 (1990) 454-466.] that selects in a data-driven way one estimate Out of a given class of estimates ordered by their variability. A serious problem with using this and similar procedures is the choice of some tuning parameters lik...
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作者：Zhou, Zhou; Wu, Wei Biao
作者单位：University of Chicago
摘要：We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear quantile estimates under a mild short-range dependence condition. Our results are applied to environmental data sets. In particular, our results can be used to address the problem of whether climate variability has changed, an important problem raised by IPCC (Intergovernmental Panel on Climate Change) in 2001.
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作者：Leeb, Hannes
作者单位：Yale University
摘要：We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important explanatory variables can be infinite, where no regularity conditions are imposed on unknown parameters, where the number of explanatory variables in a good model can be of the same order as sample size and where the number of candidate models can be of larger order t...
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作者：Singh, Aarti; Scott, Clayton; Nowak, Robert
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Michigan System; University of Michigan
摘要：Consider the problem of estimating the gamma-level set G(gamma)* = {x : f(x) > gamma} of an unknown d-dimensional density function f based on n independent observations X(1), ..., X(n) from the density. This problem has been addressed under global error criteria related to the symmetric set difference. However, in certain applications a spatially uniform mode of convergence is desirable to ensure that the estimated set is close to the target set everywhere. The Hausdorff error criterion provid...
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作者：McNeil, Alexander J.; Neslehova, Johanna
作者单位：Heriot Watt University; University of Edinburgh; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a d-monotone function. The class of d-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of d-dimensional l(1)-norm symmetric distributions that place no point mass at the origin, The d-monotone Archimedean copula generators may be characterized using a little-known integral transform of Williamson [Duke Math....
