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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure. Very recently, the first results concerning kernel random matrices with high-dimensional input data were obtained, in a setting where the data was sampled from a genuinely high-dimensional structure-similar to standard assumptions in random matrix theory. I...
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作者：Rinaldo, Alessandro; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based methods for choosing the bandwidth and we study the stability properties of density clusters. We show that a simple graph-based algorithm successfully approximates the high density clusters.
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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：Kalogeropoulos, Konstantinos; Roberts, Gareth O.; Dellaportas, Petros
作者单位：University of London; London School Economics & Political Science; University of Warwick; Athens University of Economics & Business
摘要：We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrization defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which overcomes the inherent difficulties of time change transformations is also presented. The algorithm is fast to implement and applies to models with stochastic volatility. The method...
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作者：Walther, Guenther
作者单位：Stanford University
摘要：We consider the detection of multivariate spatial clusters in the Bernoulli model with N locations, where the design distribution has weakly dependent marginals. The locations are scanned with a rectangular window with sides parallel to the axes and with varying sizes and aspect ratios. Multivariate scan statistics pose a statistical. problem due to the multiple testing over many scan windows, as well as a computational problem because statistics have to be evaluated on many windows. This pape...
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作者：Mijatovic, Aleksandar; Schneider, Paul
作者单位：Imperial College London; University of Warwick
摘要：This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem 1) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed diffusion processes. The ap...
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作者：Lee, Seunggeun; Zou, Fei; Wright, Fred A.
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：A number of settings arise in which it is of interest to predict Principal Component (PC) scores for new observations using data from an initial sample. In this paper, we demonstrate that naive approaches to PC score prediction can be substantially biased toward 0 in the analysis of large matrices. This phenomenon is largely related to known inconsistency results for sample eigenvalues and eigenvectors as both dimensions of the matrix increase. For the spiked eigenvalue model for random matric...
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作者：Jiang, Ci-Ren; Wang, Jane-Ling
作者单位：University of California System; University of California Davis
摘要：Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the first approach, both the mean and covariance functions depend on the covariate Z and time scale t while in the second approach only the mean function depends on the covariate Z. Both new approaches accommod...
