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作者：Cai, Juan-Juan; Einmahl, John H. J.; De Haan, Laurens
作者单位：Tilburg University; Universidade de Lisboa; Tilburg University
摘要：When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form {z is an element of R-d : f (z) <= beta}, where f is the joint density and beta a small number. Estimation of such an extreme risk region is difficult since it contains hardly any or no data. Using extreme value theory, we construct a natural estimator of an extreme risk region and prove a refined form of consistency, given...
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作者：Chan, Ngai Hang; Ing, Chng-Kang
作者单位：Chinese University of Hong Kong; Academia Sinica - Taiwan
摘要：In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear) stochastic regression models. The usefulness of these results is illustrated using time series models. In particular, an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving average models is obta...
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作者：Cai, T. Tony; Jiang, Tiefeng
作者单位：University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities
摘要：Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this paper the limiting laws of the coherence of an n x p random matrix in the high-dimensional setting where p can be much larger than n. Both the law of large numbers and the limiting distribution are derived. We then consider testing the bandedness of the covari...
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作者：Tibshirani, Ryan J.; Taylor, Jonathan
作者单位：Stanford University
摘要：We present a path algorithm for the generalized lasso problem. This problem penalizes the l(1) norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on solving the dual of the generalized lasso, which greatly facilitates computation of the path. For D = I (the usual lasso), we draw a connection between our approach and the well-known LARS algorithm. For an arbitrary D, we derive an unbiased estimate of the deg...
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作者：Yen, Tso-Jung
作者单位：Academia Sinica - Taiwan
摘要：We develop a method to carry out MAP estimation for a class of Bayesian regression models in which coefficients are assigned with Gaussian-based spike and slab priors. The objective function in the corresponding optimization problem has a Lagrangian form in that regression coefficients are regularized by a mixture of squared l(2) and l(0) norms. A tight approximation to the l(0) norm using majorization minimization techniques is derived, and a coordinate descent algorithm in conjunction with a...
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作者：Chen, Dong; Hall, Peter; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis; University of Melbourne
摘要：Fully nonparametric methods for regression from functional data have poor accuracy from a statistical viewpoint, reflecting the fact that their convergence rates are slower than nonparametric rates for the estimation of high-dimensional functions. This difficulty has led to an emphasis on the so-called functional linear model, which is much more flexible than common linear models in finite dimension, but nevertheless imposes structural constraints on the relationship between predictors and res...
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作者：Levy-Leduc, C.; Boistard, H.; Moulines, E.; Taqqu, M. S.; Reisen, V. A.
作者单位：Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Boston University; Universidade Federal do Espirito Santo
摘要：Let (Xi)(i >= 1) be a stationary mean-zero Gaussian process with covariances rho(k) = E(X-1 Xk+1) satisfying rho(0) = 1 and rho(k) = k(-D) L(k), where D is in (0, 1), and L is slowly varying at infinity. Consider the U-process {U-n(r), r is an element of 1} defined as U-n(r) = 1/n (n-1) Sigma(1 <= i not equal j <= n) 1{G(X-i, X-j)<= r} where I is an interval included in R, and G is a symmetric function. In this paper, we provide central and noncentral limit theorems for U-n. They are used to d...
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作者：Meister, Alexander
作者单位：University of Rostock
摘要：We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Ito process, which contains the covariance operator of the corresponding FLR model in its construction. We prove asymptotic equivalence of FLR and this white noise model in LeCam's sense under known design distribution. Moreover, we show equivalence of FLR and an empirical version of the white noise model for finite sample sizes. As an application, w...
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作者：Ait-Sahalia, Yacine; Jacod, Jean
作者单位：Princeton University; National Bureau of Economic Research; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：We propose statistical tests to discriminate between the finite and infinite activity of jumps in a semimartingale discretely observed at high frequency. The two statistics allow for a symmetric treatment of the problem: we can either take the null hypothesis to be finite activity, or infinite activity. When implemented on high-frequency stock returns, both tests point toward the presence of infinite-activity jumps in the data.
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作者：Seijo, Emilio; Sen, Bodhisattva
作者单位：Columbia University
摘要：This paper deals with the consistency of the nonparametric least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided.
