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作者：Pensky, Marianna; Sapatinas, Theofanis
作者单位：State University System of Florida; University of Central Florida; University of Cyprus
摘要：We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation. In the case when it is observed at a finite number of distinct points, the proposed functional deconvolution model can also be viewed as a ...
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作者：Malliavin, Paul; Mancino, Maria Elvira
作者单位：University of Florence
摘要：We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous serni-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price...
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作者：Arias-Castro, Ery; Donoho, David L.
作者单位：University of California System; University of California San Diego; Stanford University
摘要：Image processing researchers commonly assert that median filtering is better than linear filtering for removing noise in the presence of edges. Using a straightforward large-n decision-theory framework, this folk-theorem is seen to be false in general. We show that median filtering and linear filtering have similar asymptotic worst-case mean-squared error (MSE) when the signal-to-noise ratio (SNR) is of order 1, which corresponds to the case of constant per-pixel noise level in a digital signa...
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作者：Balakrishnan, N.; Zhao, Xingqiu
作者单位：McMaster University; Hong Kong Polytechnic University
摘要：This paper considers the problem of multi-sample nonparametric comparison of counting processes with panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and reliability experiments, for example. For the problem considered, we construct two new classes of nonparametric test statistics based on the accumulated weighted differences between the rates of increase of the estimated mean functions of the counting process...
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作者：Cai, T. Tony; Zhou, Harrison H.
作者单位：University of Pennsylvania; Yale University
摘要：A data-driven block thresholding procedure for wavelet regression is proposed and its theoretical and numerical properties are investigated. The procedure empirically chooses the block size and threshold level at each resolution level by minimizing Stein's unbiased risk estimate. The estimator is sharp adaptive over a class of Besov bodies and achieves simultaneously within a small constant factor of the minimax risk over a wide collection of Besov Bodies including both the dense and sparse ca...
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作者：Alqallaf, Fatemah; Van Aelst, Stefan; Yohai, Victor J.; Zamar, Ruben H.
作者单位：Kuwait University; Ghent University; University of Buenos Aires; University of British Columbia
摘要：We investigate the performance of robust estimates of multivariate location under nonstandard data contamination models such as componentwise outliers (i.e., contamination in each variable is independent from the other variables). This model brings up a possible new source of statistical error that we call propagation of outliers. This source of error is Unusual in the sense that it is generated by the data processing itself and takes place after the data has been collected. We define and deri...
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作者：Crambes, Christophe; Kneip, Alois; Sarda, Pascal
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; University of Bonn
摘要：The paper considers functional linear regression, where scalar responses Y-1, ... , Y-n are modeled in dependence of random functions X-1, ... , X-n. We propose a smoothing splines estimator for the functional slope parameter based on a slight modification of the usual penalty. Theoretical analysis concentrates on the error in all out-of-sample prediction of the response for a new random function Xn+1. It is shown that rates of convergence of the prediction error depend on the smoothness of th...
