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作者：Genovese, Christopher R.; Perone-Pacifico, Marco; Verdinelli, Isabella; Wasserman, Larry
作者单位：Carnegie Mellon University; Sapienza University Rome
摘要：We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.
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作者：Todorov, Viktor; Tauchen, George
作者单位：Northwestern University; Duke University
摘要：We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable Levy densities in the setting where both the time span of the data set increases, and the mesh of the observation grid decreases. The estimation is based on constructing a nonparametric estimate for the empirical Laplace transform of the stochastic scale over a given interval of time by aggregating high-frequency increments of the observed process on that time i...
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作者：Mammen, Enno; Rothe, Christoph; Schienle, Melanie
作者单位：University of Mannheim; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Humboldt University of Berlin
摘要：We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous applications, including two-stage nonparametric regression, estimation of simultaneous equation models or censored regression models. Yet so far there seems to be no general theory for their impact on the final estimator's statistical properties. Our paper p...
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作者：Rigollet, Philippe
作者单位：Princeton University
摘要：In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the parameter or even that the model on the systematic component is true. It is shown that this problem can be solved by constrained and/or penalized likelihood maximization and we deri...
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作者：Agarwal, Alekh; Negahban, Sahand; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation (sic) of the sum of an (approximately) low rank matrix Theta(star) with a second matrix Gamma(star) endowed with a complementary form of low-dimensional structure; this set-up includes many statistical models of interest, including factor analysis, multi-task regression and robust covariance estimation. We der...
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作者：Ehrlinger, John; Ishwaran, Hemant
作者单位：Cleveland Clinic Foundation; University of Miami
摘要：We consider L(2)Boosting, a special case of Friedman's generic boosting algorithm applied to linear regression under L-2-loss. We study L(2)Boosting for an arbitrary regularization parameter and derive an exact closed form expression for the number of steps taken along a fixed coordinate direction. This relationship is used to describe L(2)Boosting's solution path, to describe new tools for studying its path, and to characterize some of the algorithm's unique properties, including active set c...
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作者：Lecue, Guillaume; Mendelson, Shahar
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Technion Israel Institute of Technology
摘要：We show that empirical risk minimization procedures and regularized empirical risk minimization procedures satisfy nonexact oracle inequalities in an unbounded framework, under the assumption that the class has a subexponential envelope function. The main novelty, in addition to the boundedness assumption free setup, is that those inequalities can yield fast rates even in situations in which exact oracle inequalities only hold with slower rates. We apply these results to show that procedures b...
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作者：Wang, Qiying; Phillips, Peter C. B.
作者单位：University of Sydney; Yale University
摘要：We provide a limit theory for a general class of kernel smoothed U-statistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows for linear and nonlinear models with endogenous regressors that have autoregressive unit roots or near unit roots. The limit theory for the specification test depends on the self-intersection local time of a Gaussian process. A new weak convergence result is developed for certain partial sums of fun...
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作者：Jing, Bing-Yi; Kong, Xin-Bing; Liu, Zhi
作者单位：Hong Kong University of Science & Technology; Fudan University; Xiamen University
摘要：It is generally accepted that the asset price processes contain jumps. In fact, pure jump models have been widely used to model asset prices and/or stochastic volatilities. The question is: is there any statistical evidence from the high-frequency financial data to support using pure jump models alone? The purpose of this paper is to develop such a statistical test against the necessity of a diffusion component. The test is very simple to use and yet effective. Asymptotic properties of the pro...
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作者：Yang, Yunwen; He, Xuming
作者单位：Drexel University; University of Michigan System; University of Michigan
摘要：Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigation. This paper considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior from any fixed prior is asymptotically normal; its mean shrinks t...
