-
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...
-
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...
-
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...
-
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...
-
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...
-
作者：Nobile, A
作者单位：University of Glasgow
摘要：The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior distribution weaker than those routinely made in the literature on Bayesian analysis of finite mixtures. The inequality constraints can be used to perform an internal consistency check of MCMC estimates of the posterior distribution of k and to provide improved es...
-
作者：Fuh, CD
作者单位：Academia Sinica - Taiwan
摘要：Let xi(0),xi(1),...,xi(omega-1) be observations from the hidden Markov model with probability distribution P(theta)0, and let xi(omega), xi(omega+1),... be observations from the hidden Markov model with probability distribution P(theta)1. The parameters theta(0) and theta(1) are given, while the change point omega is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from P(theta)0 to P(theta)1, but to avoid false alarms. Specifically, we seek a stoppi...
-
作者：Hall, P; Ooi, H
作者单位：Australian National University
摘要：We discuss properties of two methods for ascribing probabilities to the shape of a probability distribution. One is based on the idea of counting the number of modes of a bootstrap version of a standard kernel density estimator. We argue that the simplest form of that method suffers from the same difficulties that inhibit level accuracy of Silverman's bandwidth-based test for modality: the conditional distribution of the bootstrap form of a density estimator is not a good approximation to the ...
-
作者：Fan, JQ; Zhang, J
作者单位：Princeton University; Chinese University of Hong Kong; University of Kent; Chinese Academy of Sciences
摘要：Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing norparametic hypotheses about nonparametric functions. The likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family. We extend their work to the case where the error distribution is completely unspecified via newly proposed sieve empirical likeli...
-
作者：Cator, EA
作者单位：Delft University of Technology
摘要：In recent years a popular nonparametric model for coarsened data is an assumption on the coarsening mechanism called coarsening at random (CAR). It has been conjectured in several papers that this assumption cannot be tested by the data, that is, the assumption does not restrict the possible distributions of the data. In this paper we will show that this conjecture is not always true; an example will be current status data. We will also give conditions when the conjecture is true, and in doing...
