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作者：Whiteley, Nick; Lee, Anthony
作者单位：University of Bristol; University of Warwick
摘要：We investigate sampling laws for particle algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. Among a broad class of candidates we characterize the essentially unique family of particle system transition kernels which is optimal with respect to an asymptotic-in-time variance growth rate criterion. The sampling structure of the algorithm defined by these optimal transitions turns out to be only subtly different...
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作者：Fasy, Brittany Terese; Lecci, Fabrizio; Rinaldo, Alessandro; Wasserman, Larry; Balakrishnan, Sivaraman; Singh, Aarti
作者单位：Tulane University; Carnegie Mellon University; Carnegie Mellon University
摘要：Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be topological noise, and those with a long lifetime are considered to be topological signal. In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence sets that allow us to sepa...
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作者：Wang, Zhaoran; Liu, Han; Zhang, Tong
作者单位：Princeton University; Rutgers University System; Rutgers University New Brunswick
摘要：We provide theoretical analysis of the statistical and computational properties of penalized M-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized linear models with nonconvex.regularization and sparse elliptical random design regression. For these problems, it is intractable to calculate the global solution due to the noncon...
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作者：Bull, Adam D.
作者单位：University of Cambridge
摘要：In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling. We give a new estimate of the normalised volatility or time change in this model, which obtains minimax convergence rates, and is unaffected by infinite-variation jumps. In the semimartingale model, our estimate remains accurate for the normalised volatility, obtaining convergence rates as goo...
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作者：Zhou, Zhou
作者单位：University of Toronto
摘要：We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted V-statistics through the angle of Fourier analysis. The established theory for V-statistics provides a unified treatment for many important time and spectral domain problems in the analysis of nonstationary time series, ranging from nonparametric estimation to the inference ...
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作者：Bibinger, Markus; Hautsch, Nikolaus; Malec, Peter; Reiss, Markus
作者单位：Humboldt University of Berlin; University of Vienna; Humboldt University of Berlin
摘要：An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semi-parametric efficiency is established in the Cramer-Rao sense. Main findings are ...
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作者：Arias-Castro, Ery; Verzelen, Nicolas
作者单位：University of California System; University of California San Diego; INRAE
摘要：We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on N nodes. Under the null hypothesis, the graph is a realization of an Erdos-Renyi graph with probability p(0). Under the (composite) alternative, there is an unknown subgraph of n nodes where the probability of connection is P-1 > p(0). We derive a detection lower bound for detect...
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作者：Guo, Wenge; He, Li; Sarkar, Sanat K.
作者单位：New Jersey Institute of Technology; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：The probability of false discovery proportion (FDP) exceeding gamma is an element of [0, 1), defined as gamma-FDP, has received much attention as a measure of false discoveries in multiple testing. Although this measure has received acceptance due to its relevance under dependency, not much progress has been made yet advancing its theory under such dependency in a nonasymptotic setting, which motivates our research in this article. We provide a larger class of procedures containing the stepup ...
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作者：Zhou, Shuheng
作者单位：University of Michigan System; University of Michigan
摘要：Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one is able to recover the graphs and covariance matrices with a single random matrix from the matrix variate normal distribution. Our method extends, with suitable adaptation, to t...
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作者：Jiang, Ci-Ren; Yu, Wei; Wang, Jane-Ling
作者单位：Academia Sinica - Taiwan; Roche Holding; Roche Holding USA; Genentech; University of California System; University of California Davis
摘要：Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferro and Yao [Statistics 37 (2003) 475-488, Statist. Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755] to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of ...
