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作者：Duchi, John; Khosravi, Khashayar; Ruan, Feng
作者单位：Stanford University
摘要：We provide a unifying view of statistical information measures, multiway Bayesian hypothesis testing, loss functions for multiclass classification problems and multidistribution f-divergences, elaborating equivalence results between all of these objects, and extending existing results for binary outcome spaces to more general ones. We consider a generalization of f-divergences to multiple distributions, and we provide a constructive equivalence between divergences, statistical information (in ...
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作者：Mak, Simon; Joseph, V. Roshan
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：This paper introduces a new way to compact a continuous probability distribution F into a set of representative points called support points. These points are obtained by minimizing the energy distance, a statistical potential measure initially proposed by Szekely and Rizzo [InterStat 5 (2004) 1-6] for testing goodness-of-fit. The energy distance has two appealing features. First, its distance-based structure allows us to exploit the duality between powers of the Euclidean distance and its Fou...
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作者：Wu, Hau-Tieng; Wu, Nan
作者单位：Duke University; Duke University; University of Toronto
摘要：Since its introduction in 2000, Locally Linear Embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of LLE under the manifold setup. We show that for a general manifold, asymptotically we may not obtain the Laplace-Beltrami operator, and the result may depend on nonuniform sampling unless a correct regularization is chosen. We also derive the corresponding kernel function, which indicates that LLE is not a Markov process. A comparison with other commonly...
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作者：Zhang, Yichong
作者单位：Singapore Management University
摘要：This paper establishes an asymptotic theory and inference method for quantile treatment effect estimators when the quantile index is close to or equal to zero. Such quantile treatment effects are of interest in many applications, such as the effect of maternal smoking on an infant's adverse birth outcomes. When the quantile index is close to zero, the sparsity of data jeopardizes conventional asymptotic theory and bootstrap inference. When the quantile index is zero, there are no existing infe...
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作者：Groeneboom, Piet; Hendrickx, Kim
作者单位：Delft University of Technology; Hasselt University
摘要：We construct root n-consistent and asymptotically normal estimates for the finite dimensional regression parameter in the current status linear regression model, which do not require any smoothing device and are based on maximum likelihood estimates (MLEs) of the infinite dimensional parameter. We also construct estimates, again only based on these MLEs, which are arbitrarily close to efficient estimates, if the generalized Fisher information is finite. This type of efficiency is also derived ...
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作者：Pan, Wenliang; Tian, Yuan; Wang, Xueqin; Zhang, Heping
作者单位：Sun Yat Sen University; Sun Yat Sen University; Yale University
摘要：In this paper, we first introduce Ball Divergence, a novel measure of the difference between two probability measures in separable Banach spaces, and show that the Ball Divergence of two probability measures is zero if and only if these two probability measures are identical without any moment assumption. Using Ball Divergence, we present a metric rank test procedure to detect the equality of distribution measures underlying independent samples. It is therefore robust to outliers or heavy-tail...
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作者：He, Yuanzhen; Cheng, Ching-Shui; Tang, Boxin
作者单位：Beijing Normal University; Academia Sinica - Taiwan; Simon Fraser University
摘要：Strong orthogonal arrays were recently introduced and studied in He and Tang [Biometrika 100 (2013) 254-260] as a class of space-filling designs for computer experiments. To enjoy the benefits of better space-filling properties, when compared to ordinary orthogonal arrays, strong orthogonal arrays need to have strength three or higher, which may require run sizes that are too large for experimenters to afford. To address this problem, we introduce a new class of arrays, called strong orthogona...
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作者：Rao, Suhasini Subba
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：A class of Fourier based statistics for irregular spaced spatial data is introduced. Examples include the Whittle likelihood, a parametric estimator of the covariance function based on the L-2-contrast function and a simple nonparametric estimator of the spatial autocovariance which is a nonnegative function. The Fourier based statistic is a quadratic form of a discrete Fourier-type transform of the spatial data. Evaluation of the statistic is computationally tractable, requiring O(nb) operati...
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作者：Koul, Hira L.; Song, Weixing; Zhu, Xiaoqing
作者单位：Michigan State University; Kansas State University
摘要：This paper investigates a class of goodness-of-fit tests for fitting an error density in linear regression models with measurement error in covariates. Each test statistic is the integrated square difference between the deconvolution kernel density estimator of the regression model error density and a smoothed version of the null error density, an analog of the so-called Bickel and Rosenblatt test statistic. The asymptotic null distributions of the proposed test statistics are derived for both...
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作者：Tian, Xiaoying; Taylor, Jonathan
作者单位：Stanford University
摘要：Inspired by sample splitting and the reusable holdout introduced in the field of differential privacy, we consider selective inference with a randomized response. We discuss two major advantages of using a randomized response for model selection. First, the selectively valid tests are more powerful after randomized selection. Second, it allows consistent estimation and weak convergence of selective inference procedures. Under independent sampling, we prove a selective (or privatized) central l...
