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作者：Chan, Ngai Hang; Huang, Shih-Feng; Ing, Ching-Kang
作者单位：Chinese University of Hong Kong; National University Kaohsiung; Academia Sinica - Taiwan
摘要：A moment bound for the normalized conditional-sum-of-squares (CSS) estimate of a general autoregressive fractionally integrated moving average (ARFIMA) model with an arbitrary unknown memory parameter is derived in this paper. To achieve this goal, a uniform moment bound for the inverse of the normalized objective function is established. An important application of these results is to establish asymptotic expressions for the one-step and multi-step mean squared prediction errors (MSPE) of the...
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作者：Shang, Zuofeng; Cheng, Guang
作者单位：University of Notre Dame; Purdue University System; Purdue University
摘要：This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. Statist. Math. 37 (1966) 577-580]. Equipped with this tool, we develop four interconnected procedures for inference: (i) pointwise confidence interval; (ii) local likelihood ratio...
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作者：Azizyan, Martin; Singh, Aarti; Wasserman, Larry
作者单位：Carnegie Mellon University; Carnegie Mellon University
摘要：Semisupervised methods are techniques for using labeled data (X-1, Y-1), ..., (X-n, Y-n) together with unlabeled data Xn+1, ..., X-N to make predictions. These methods invoke some assumptions that link the marginal distribution P-X of X to the regression function f(x). For example, it is common to assume that f is very smooth over high density regions of P-X. Many of the methods are ad-hoc and have been shown to work in specific examples but are lacking a theoretical foundation. We provide a m...
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作者：Perchet, Vianney; Rigollet, Philippe
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Princeton University
摘要：We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows for dynamically changing rewards that better describe applications where side information is available We adopt a nonparametric model where the expected rewards are smooth functions of the covariate and where the hardness of the problem is captured by a margi...
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作者：Fan, Yingying; Jin, Jiashun; Yao, Zhigang
作者单位：University of Southern California; Carnegie Mellon University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix Sigma, where the precision matrix Omega = Sigma(-1) is unknown but is presumably sparse. The useful features, also unknown, are sparse and each contributes weakly (i.e., rare and weak) to the classification decision. By obtaining a reasonably good estimate of Omega, we formulate the setting as a linear regre...
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作者：Sejdinovic, Dino; Sriperumbudur, Bharath; Gretton, Arthur; Fukumizu, Kenji
作者单位：University of London; University College London; University of Cambridge; Max Planck Society; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning. In the case where the energy distance is computed with a semimetric of negative type, a positive definite ke...
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作者：Berthet, Quentin; Rigollet, Philippe
作者单位：Princeton University
摘要：We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels, and it performs well on simulated datasets....
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作者：Buecher, Axel; Vetter, Mathias
作者单位：Ruhr University Bochum
摘要：In this paper nonparametric methods to assess the multivariate Levy measure are introduced. Starting from high-frequency observations of a Levy process X, we construct estimators for its tail integrals and the Pareto-Levy copula and prove weak convergence of these estimators in certain function spaces. Given n observations of increments over intervals of length Delta(n), the rate of convergence is k(n)(-1/2) for k(n) = n Delta(n) which is natural concerning inference on the Levy measure. Besid...
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作者：Jacod, Jean; Podolskij, Mark
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ruprecht Karls University Heidelberg
摘要：In this paper, we present a test for the maximal rank of the matrix-valued volatility process in the continuous Ito semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Ito semimartingale, which opens the way for rank testing. We develop the complete limit theory for the test statistic and apply it to various null and alternative hypotheses. Finally, we demonstrate a homoscedasticity test for the rank process.
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作者：Schmidt-Hieber, Johannes; Munk, Axel; Duembgen, Lutz
作者单位：Vrije Universiteit Amsterdam; University of Gottingen; Max Planck Society; University of Bern
摘要：We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investi...
