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作者：van der Vaart, A. W.; van Zanten, J. H.
作者单位：Vrije Universiteit Amsterdam
摘要：We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing all inverse Gamma bandwidth. The procedure is studied from a frequentist perspective in three statistical settings involving replicated observations (density estimation, regression and classification). We prove that the resulting posterior distribution shrinks to th...
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作者：Zhang, Cun-Hui; Zhang, Zhiyi
作者单位：Rutgers University System; Rutgers University New Brunswick; University of North Carolina; University of North Carolina Charlotte
摘要：This paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by Good [Biometrica 40 (1953) 237-264]. This new necessary and sufficient condition extends the validity of the asymptotic normality beyond the previously proven cases.
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作者：Cui, Xia; Guo, Wensheng; Lin, Lu; Zhu, Lixing
作者单位：Shandong University; Hong Kong Baptist University; University of Pennsylvania; East China Normal University
摘要：In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods for the linear setting cannot be directly employed. To attack this problem, we propose estimating the distorting functions by nonparametrically regressing the predictors and response on the distorting covariate; then, nonlinear least squares estimators for t...
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作者：Shi, Tao; Belkin, Mikhail; Yu, Bin
作者单位：University System of Ohio; Ohio State University; University System of Ohio; Ohio State University; University of California System; University of California Berkeley
摘要：This paper focuses on obtaining clustering information about a distribution from its i.i.d. samples. We develop theoretical results to understand and use clustering information contained in the eigenvectors of data adjacency matrices based on a radial kernel function with a sufficiently fast tail decay. In particular, we provide population analyses to gain insights into which eigenvectors should be used and when the clustering information for the distribution can be recovered from the sample. ...
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作者：Wasserman, Larry; Roeder, Kathryn
作者单位：Carnegie Mellon University
摘要：This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression methods. In the first stage we fit a set of candidate models. In the second stage we select one model by cross-validation. In the third stage we use hypothesis testing to eliminate some variables. We refer to the first two stages as screening and the last stage as...
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作者：Brown, Lawrence D.; Greenshtein, Eitan
作者单位：University of Pennsylvania; Duke University
摘要：We consider the classical problem of estimating a vector mu = (mu(1,) ..., mu(n)) based on independent observations Yi similar to N(mu(i), 1), i = 1, ..., n. Suppose mu(i), i = 1, ..., n are independent realizations from a completely unknown G. We suggest an easily computed estimator (mu) over cap, such that the ratio of its risk E((mu) over cap - mu)(2) with that of the Bayes procedure approaches 1. A related compound decision result is also obtained. Our asymptotics is of a triangular array;...
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作者：Ait-Sahalia, Yacine; Jacod, Jean
作者单位：Princeton University; National Bureau of Economic Research; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We propose a new test to determine whether jumps are present in asset returns or other discretely sampled processes. As the sampling interval tends to 0, our test statistic converges to I if there are jumps, and to another deterministic and known value (such as 2) if there are no jumps. The test is valid 4 for all Ito semi martingales, depends neither on the law of the process nor on the coefficients of the equation which it solves, does not require a preliminary estimation of these coefficien...
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作者：Zhou, Yong; Liang, Hua
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Shanghai University of Finance & Economics; University of Rochester
摘要：We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square based estimation procedures are developed for parametric and nonparametric components after we calibrate the error-prone covariates. Asymptotic properties of the proposed estimators are established. We also propose the profile least-square based ratio test and Wald test to identify significant parametric and...
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作者：Du, Juan; Zhang, Hao; Mandrekar, V. S.
作者单位：Michigan State University; Purdue University System; Purdue University
摘要：When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. Under the assumption that data are collected along a line in a bounded region, we investigate how the tapering affects the asymptotic efficiency of the maximum likelihood estimator (MLE) for the microergodic parameter in the Matern covariance func...
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作者：Juditsky, Anatoli B.; Nemirovski, Arkadi S.
作者单位：University System of Georgia; Georgia Institute of Technology; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria
摘要：The problem we concentrate on is as follows: given (1) a convex compact set X in R-n, an affine mapping x bar right arrow A(x), a parametric family {p(mu)(.)} of probability densities and (2) N i.i.d. observations of the random variable omega, distributed with the density p(A(x)) (.) for some (unknown) x is an element of X, estimate the value g(T)x of a given linear form at x. For several families {p(mu)(.)} with no additional assumptions on X and A, we develop computationally efficient estima...
