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作者：Hall, Peter; Jin, Jiashun
作者单位：University of Melbourne; University of California System; University of California Davis; Carnegie Mellon University
摘要：Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables are correlated. In this paper we show that, by exploiting the nature of the correlation, performance can be improved by using a modified approach which exploits the potential advantages that correlation has to offer. Indeed, it turns out that the case of in...
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作者：Samworth, R. J.; Wand, M. P.
作者单位：University of Cambridge; University of Cambridge; University of Wollongong
摘要：We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.
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作者：Jiang, Jiancheng; Fan, Yingying; Fan, Jianqing
作者单位：University of North Carolina; University of North Carolina Charlotte; University of Southern California; Princeton University
摘要：Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimation. The former is designed for highly correlated covariates, and the latter is useful for nonhighly correlated covariates. Asymptotic normalities of the proposed estimators are established. Simulat...
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作者：Sullivant, Seth; Talaska, Kelli; Draisma, Jan
作者单位：North Carolina State University; University of Michigan System; University of Michigan; Eindhoven University of Technology
摘要：Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the covariance matrix have small rank for a general class of mixed graphs that includes directed acyclic and undirected graphs as special cases. Our new trek separation criterion genera...
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作者：Olshen, Richard A.; Rajaratnam, Bala
作者单位：Stanford University; Stanford University; Stanford University
摘要：Standard statistical techniques often require transforming data to have mean 0 and standard deviation I. Typically, this process of standardization or normalization is applied across subjects when each subject produces a single number. High throughput genomic and financial data often come as rectangular arrays where each coordinate in one direction concerns subjects who might have different status (case or control, say), and each coordinate in the other designates outcome for a specific featur...
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作者：Jacod, Jean; Podolskij, Mark; Vetter, Mathias
作者单位：Universite Paris Cite; Sorbonne Universite; Swiss Federal Institutes of Technology Domain; ETH Zurich; Ruhr University Bochum
摘要：This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634-658, Stochastic Process. Appl. 119 (2009) 2249-2276]) and provides consistent estimates for various characteristics of general semimartingales. Furthermore, we prove the associated multidimensional (stable) central limit theorems. As expected, we find central limit t...
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作者：Jensen, Jens Ledet
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作者：Liu, Yukun; Chen, Jiahua
作者单位：East China Normal University; University of British Columbia; Nankai University
摘要：Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective at addressing both ...
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作者：Park, Byeong U.; Jeong, Seok-Oh; Simar, Leopold
作者单位：Seoul National University (SNU); Hankuk University Foreign Studies; Hankuk University Foreign Studies
摘要：Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of inputs x outputs in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the inputs x outputs space. So far, only the statistical properties of the smallest convex pol...
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作者：Wong, Wing H.; Ma, Li
作者单位：Stanford University
摘要：We introduce an extension of the Polya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting optional Polya tree distribution has large support in total variation topology and yields posterior distributions that are also optiona...
