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作者：Konig, Claudia; Munk, Axel; Werner, Frank
作者单位：University of Gottingen
摘要：We consider the problem of finding anomalies in a d-dimensional field of independent random variables {Y-i}(i is an element of{1,...,n}d), each distributed according to a one-dimensional natural exponential family F = {F-theta}(theta is an element of Theta). Given some baseline parameter theta(0) is an element of Theta, the field is scanned using local likelihood ratio tests to detect from a (large) given system of regions R those regions R subset of {1, ..., n}(d) with theta(i) not equal thet...
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作者：Yang, Yun; Pati, Debdeep; Bhattacharya, Anirban
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Texas A&M University System; Texas A&M University College Station
摘要：We provide statistical guarantees for a family of variational approximations to Bayesian posterior distributions, called alpha-VB, which has close connections with variational approximations of tempered posteriors in the literature. The standard variational approximation is a special case of alpha-VB with alpha = 1. When alpha is an element of (0, 1], a novel class of variational inequalities are developed for linking the Bayes risk under the variational approximation to the objective function...
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作者：Shen, Jinqi; Hsing, Tailen
作者单位：University of Michigan System; University of Michigan
摘要：This paper considers a wide range of issues concerning the estimation of the Hurst function of a multifractional Brownian motion when the process is observed on a regular grid. A theoretical lower bound for the minimax risk of this inference problem is established for a wide class of smooth Hurst functions. We also propose a new nonparametric estimator and show that it is rate optimal. Implementation issues of the estimator including how to overcome the presence of a nuisance parameter and cho...
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作者：Ekvall, Karl Oskar; Jones, Galin L.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full data. It requires neither that the data consist of independent observations, nor that the observations can be modeled as a stationary stochastic process. Compared to existing asymptotic theory using the idea of subsets, we substantially weaken the assumptions, b...
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作者：Ghosal, Promit; Mukherjee, Sumit
作者单位：Columbia University
摘要：We study joint estimation of the inverse temperature and magnetization parameters (beta, B) of an Ising model with a nonnegative coupling matrix A(n) of size n x n, given one sample from the Ising model. We give a general bound on the rate of consistency of the bi-variate pseudo-likelihood estimator. Using this, we show that estimation at rate n(-1/2) is always possible if A(n) is the adjacency matrix of a bounded degree graph. If A(n) is the scaled adjacency matrix of a graph whose average de...
