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作者：Goldenshluger, Alexander; Lepski, Oleg
作者单位：University of Haifa; Aix-Marseille Universite
摘要：We address the problem of density estimation with L(s)(-)loss by selection of kernel estimators. We develop a selection procedure and derive corresponding L-s-risk oracle inequalities. It is shown that the proposed selection rule leads to the estimator being minimax adaptive over a scale of the anisotropic Nikol'skii classes. The main technical tools used in our derivations are uniform bounds on the L-s-norms of empirical processes developed recently by Goldenshluger and Lepski [Ann. Probab. (...
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作者：Kirch, Claudia; Politis, Dimitris N.
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of California System; University of California San Diego
摘要：A new time series bootstrap scheme, the time frequency toggle (TFT)-bootstrap, is proposed. Its basic idea is to bootstrap the Fourier coefficients of the observed time series, and then to back-transform them to obtain a bootstrap sample in the time domain. Related previous proposals, such as the surrogate data approach, resampled only the phase of the Fourier coefficients and thus had only limited validity. By contrast, we show that the appropriate resampling of phase and magnitude, in additi...
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作者：Anevski, Dragi; Soulier, Philippe
作者单位：Universite Paris Nanterre
摘要：We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.
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作者：Jimenez, Raul; Yukich, J. E.
作者单位：Universidad Carlos III de Madrid; Lehigh University
摘要：The estimation of surface integrals on the boundary of an unknown body is a challenge for nonparametric methods in statistics, with powerful applications to physics and image analysis, among other fields. Provided that one can determine whether random shots hit the body, Cuevas et al. [Ann. Statist. 35 (2007) 1031-1051] estimate the boundary measure (the boundary length for planar sets and the surface area for 3-dimensional objects) via the consideration of shots at a box containing the body. ...
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作者：Stein, Michael L.
作者单位：University of Chicago
摘要：When using optimal linear prediction to interpolate point observations of a mean square continuous stationary spatial process, one often finds that the interpolant mostly depends on those observations located nearest to the predictand. This phenomenon is called the screening effect. However, there are situations in which a screening effect does not hold in a reasonable asymptotic sense, and theoretical support for the screening effect is limited to some rather specialized settings for the obse...
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作者：Hoffmann, Marc; Nickl, Richard
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University of Cambridge
摘要：The problem of existence of adaptive confidence bands for an unknown density f that belongs to a nested scale of Holder classes over R or [0, 1] is considered. Whereas honest adaptive inference in this problem is impossible already for a pair of Holder balls Sigma (r), Sigma(s), r not equal s, of fixed radius, a non-parametric distinguishability condition is introduced under which adaptive confidence bands can be shown to exist. It is further shown that this condition is necessary and sufficie...
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作者：Papavasiliou, Anastasia; Ladroue, Christophe
作者单位：University of Warwick; University of Crete; University of Bristol
摘要：We construct the expected signature matching estimator for differential equations driven by rough paths and we prove its consistency and asymptotic normality. We use it to estimate parameters of a diffusion and a fractional diffusions, that is, a differential equation driven by fractional Brownian motion.
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作者：Liao, Yuan; Jiang, Wenxin
作者单位：Princeton University; Northwestern University
摘要：This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter g(0). We estimate it in a quasi-Bayesian way, based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thin-tail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior with nonshrinking v...
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作者：Obozinski, Guillaume; Wainwright, Martin J.; Jordan, Michael I.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：In multivariate regression, a K-dimensional response vector is regressed upon a common set of p covariates, with a matrix B* is an element of R-pxK of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the l(1)/l(2) norm is used for support union recovery, or recovery of the set of s rows for which B* is nonzero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of ...
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作者：Dick, Josef
作者单位：University of New South Wales Sydney
摘要：We study a random sampling technique to approximate integrals f[0,1](s) f (x) dx by averaging the function at some sampling points. We focus on cases where the integrand is smooth, which is a problem which occurs in statistics. The convergence rate of the approximation error depends on the smoothness of the function f and the sampling technique. For instance, Monte Carlo (MC) sampling yields a convergence of the root mean square error (RMSE) of order N(-1/2) (where N is the number of samples) ...
