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作者：Gobet, E; Hoffmann, M; Reiss, M
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Universite Paris Cite; Sorbonne Universite; Humboldt University of Berlin
摘要：We study the problem of estimating the coefficients of a diffusion (X-t, t greater than or equal to 0); the estimation is based on discrete data X-nDelta, n = 0, 1,..., N. The sampling frequency Delta(-1) is constant, and asymptotics are taken as the number N of observations tends to infinity. We prove that the problem of estimating both the diffusion coefficient (the volatility) and the drift in a nonparametric setting is ill-posed: the minimax rates of convergence for Sobolev constraints and...
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作者：Goldenshluger, A; Zeevi, A
作者单位：University of Haifa; Columbia University
摘要：This article pursues a statistical study of the Hough transform, the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose objective is to find the line that best fits a set of planar points. In particular, we establish strong consistency and rates of convergence, and characterize the limiting distribution of the Hough transform estimator. While the convergence rates are seen to b...
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作者：Rosset, S; Zhu, J
作者单位：International Business Machines (IBM); IBM USA; University of Michigan System; University of Michigan
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作者：Freund, Y; Schapire, RE
作者单位：Columbia University; Princeton University
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作者：Butler, RW; Wood, ATA
作者单位：Colorado State University System; Colorado State University Fort Collins; University of Nottingham
摘要：We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the application of saddlepoint approximations to certain distributions determined by truncated random variables. Two important statistical applications are the following: the approximation of certain multivariate cumulative distribution functions; and the approxim...
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作者：Hall, P; Penev, S
作者单位：Australian National University; University of London; London School Economics & Political Science; University of New South Wales Sydney
摘要：We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator, and decreasing it when, again using thresholded terms as an empirical guide, signal complexity is judged to have decreased. Through sampling in this way the algorithm is able to accurately recover relatively complex signals without increasing the long-run ave...
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作者：Turlach, BA
作者单位：University of Western Australia
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作者：Shimodaira, H
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：Approximately unbiased tests based on bootstrap probabilities are considered for the exponential family of distributions with unknown expectation parameter vector, where the null hypothesis is represented as an arbitrary-shaped region with smooth boundaries. This problem has been discussed previously in Efron and Tibshirani [Ann. Statist. 26 (1998) 1687-1718], and a corrected p-value with second-order asymptotic accuracy is calculated by the two-level bootstrap of Efron, Halloran and Holmes [P...
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作者：Aït-Sahalia, Y; Mykland, PA
作者单位：Princeton University; National Bureau of Economic Research; University of Chicago
摘要：We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimators. As a special case, our results apply to the situation where the data are discretely sampled at a f...
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作者：Nordman, DJ; Lahiri, SN
作者单位：University of Wisconsin System; Iowa State University
摘要：We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance estimator, which yields an expression for the theoretically optimal block size. The optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as characteristics of the underlying random field. Final expression...
