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作者：Dette, Holger; Melas, Viatcheslav B.; Shpilev, Petr
作者单位：Ruhr University Bochum; Saint Petersburg State University
摘要：This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57-70]. T-optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution to this problem we propose a Bayesian and standardized maximin approach to construct robust and efficient d...
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作者：Zhang, Li
作者单位：Microsoft
摘要：We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints (lq constraint with 0 <= 1) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic factor of the optimal for any design matrix. Then by utilizing a semi-definite programming relaxation te...
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作者：Hall, Peter; Horowitz, Joel
作者单位：University of Melbourne; University of California System; University of California Davis; Northwestern University
摘要：Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches, and others based on nonstandard smoothing methods...
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作者：Li, Jia; Todorov, Viktor; Tauchen, George
作者单位：Duke University; Northwestern University
摘要：We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Ito semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a kernel-based estim...
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作者：Amini, Arash A.; Chen, Aiyou; Bickel, Peter J.; Levina, Elizaveta
作者单位：University of Michigan System; University of Michigan; Alphabet Inc.; Google Incorporated; University of California System; University of California Berkeley
摘要：Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees. We show that the algorithms perform well under a range of settings, including on very sparse networks, and illustrate on the e...
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作者：Jiang, Tiefeng; Yang, Fan
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Minnesota System; University of Minnesota Twin Cities
摘要：For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been extensively studied in multivariate analysis, and their limiting distributions under the null hypothesis were proved to be chi-square distributions as n goes to infinity and p remains fixed. In this paper, we consider the high-dimensional case where both p and n ...
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作者：Zhang, Rongmao; Peng, Liang; Wang, Ruodu
作者单位：Zhejiang University; University System of Georgia; Georgia Institute of Technology; University of Waterloo
摘要：Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded...
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作者：Bickel, Peter; Choi, David; Chang, Xiangyu; Zhang, Hai
作者单位：University of California System; University of California Berkeley; Carnegie Mellon University; Xi'an Jiaotong University; Northwest University Xi'an
摘要：Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The result also applies to various sub-models of the stochastic blockmodel found in the literature.
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作者：Yamagata, Koichi; Fujiwara, Akio; Gill, Richard D.
作者单位：University of Osaka; Leiden University - Excl LUMC; Leiden University
摘要：We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.
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作者：Berthet, Quentin; Rigollet, Philippe
作者单位：Princeton University
摘要：We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to be NP-complete in general, and we describe a computationally efficient alternative test using convex relaxations. Our relaxation is also proved to detect sparse principal components at near optimal detection levels, and it performs well on simulated datasets....
