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作者：Hall, Peter; Horowitz, Joel
作者单位：University of Melbourne; University of California System; University of California Davis; Northwestern University
摘要：Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches, and others based on nonstandard smoothing methods...
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作者：Dette, Holger; Schorning, Kirsten
作者单位：Ruhr University Bochum
摘要：In a recent paper Yang and Stufken [Ann. Statist. 40 (2012a) 1665-1685] gave sufficient conditions for complete classes of designs for nonlinear regression models. In this note we demonstrate that there is an alternative way to validate this result. Our main argument utilizes the fact that boundary points of moment spaces generated by Chebyshev systems possess unique representations.
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作者：Jacod, Jean; Rosenbaum, Mathieu
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：We consider a multidimensional Ito semimartingale regularly sampled on [0, t] at high frequency 1/Delta(n), with Delta(n) going to zero. The goal of this paper is to provide an estimator for the integral over [0, t] of a given function of the volatility matrix. To approximate the integral, we simply use a Riemann sum based on local estimators of the pointwise volatility. We show that although the accuracy of the pointwise estimation is at most Delta(1/4)(n), this procedure reaches the parametr...
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作者：Suzuki, Taiji; Sugiyama, Masashi
作者单位：University of Tokyo; Institute of Science Tokyo; Tokyo Institute of Technology
摘要：We investigate the learning rate of multiple kernel learning (MKL) with l(1) and elastic-net regularizations. The elastic-net regularization is a composition of an l(1)-regularizer for inducing the sparsity and an l(2)-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large, but the number of nonzero components of the ground truth is relatively small, and show sharper convergence rates than the learning rates have ever shown for both ...
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作者：Bull, Adam D.
作者单位：University of Cambridge
摘要：While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this, paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function classes, it likewise...
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作者：Zheng, Wei
作者单位：Indiana University System; Indiana University Indianapolis
摘要：Subject dropout is very common in practical applications of crossover designs. However, there is very limited design literature taking this into account. Optimality results have not yet been well established due to the complexity of the problem. This paper establishes feasible, as well as necessary and sufficient conditions for a crossover design to be universally optimal in approximate design theory in the presence of subject dropout. These conditions are essentially linear equations with res...
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作者：Mukerjee, Rahul; Tang, Boxin
作者单位：Indian Institute of Management (IIM System); Indian Institute of Management Calcutta; Simon Fraser University
摘要：Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number of factors. This is in contrast to existing theoretical results which work only for a relatively small number of factors. While the use of imaginary numbers to represent the Gray map associated with QC designs facilitates the derivation, establishing a link w...
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作者：Zhong, Ping-Shou; Chen, Song Xi; Xu, Minya
作者单位：Michigan State University; Peking University; Peking University; Iowa State University
摘要：We consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise dependence. The two alternative test statistics are constructed by first thresholding L-1 and L-2 statistics based on the sample means, respectively, followed by maximizing over a range of thresholding levels to make the tests adaptive to the unknown signal...
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作者：Panaretos, Victor M.; Tavakoli, Shahin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which generalises the notion of a spectral density matrix to the functional setting, and characterises the second-order dynamics of the process. Our main tool is the functional Discrete Fourier Transform (fDFT). We derive an asymptotic Gaussian repres...
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作者：Pensky, Marianna
作者单位：State University System of Florida; University of Central Florida
摘要：The objective of the present paper is to introduce the concept of a spatially inhomogeneous linear inverse problem where the degree of ill-posedness of operator Q depends not only on the scale but also on location. In this case, the rates of convergence are determined by the interaction of four parameters, the smoothness and spatial homogeneity of the unknown function f and degrees of ill-posedness and spatial inhomogeneity of operator Q. Estimators obtained in the paper are based either on wa...
