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作者：Chatterjee, Sourav; Diaconis, Persi
作者单位：Stanford University
摘要：We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and Varadhan [European J. Combin. 32 (2011) 1000-1017]. The theory explains a host of difficulties encountered by applied workers: many distinct models have essentially the same MLE, rendering the problems practically ill-posed. We give the first rigorous proofs of d...
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作者：Zhao, Junlong; Leng, Chenlei; Li, Lexin; Wang, Hansheng
作者单位：Beihang University; University of Warwick; National University of Singapore; North Carolina State University; Peking University
摘要：Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our p...
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作者：Braess, Dietrich; Dette, Holger
作者单位：Ruhr University Bochum
摘要：The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the optimality criterion criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289-303]. The numerical construction of optimal designs is very hard and challenging, if the number of pairwise comparisons is larger than 2. It is demonstrated that optimal designs with respect to this type of criteria can be obtained by solving (nonlinear) vector-v...
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作者：Draisma, Jan; Kuhnt, Sonja; Zwiernik, Piotr
作者单位：Eindhoven University of Technology; Dortmund University of Technology; University of California System; University of California Berkeley
摘要：Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite exponential transformation families. We reveal this structure by explicitly describing, for any undirected graph, the (maximal) matrix group acting on the space of concentration matrices in the model. The continuous part of this group is captured by a poset n...
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作者：Chen, Jiahua; Liu, Yukun
作者单位：University of British Columbia; East China Normal University
摘要：Population quantiles and their functions are important parameters in many applications. For example, the lower quantiles often serve as crucial quality indices for forestry products. Given several independent samples from populations satisfying the density ratio model, we investigate the properties of empirical likelihood (EL) based inferences. The induced EL quantile estimators are shown to admit a Bahadur representation that leads to asymptotically valid confidence intervals for functions of...
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作者：Di Nardo, E.; McCullagh, P.; Senato, D.
作者单位：University of Basilicata; University of Chicago
摘要：Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions, k-statistics and polykays. We construct spectral k-statistics as unbiased estimators of cumulants of trace powers of a suitable random matrix. Moreover we define normalized spectral polykays in such a way that when the sampling is from an infinite popu...
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作者：Field, Chris; Robinson, John
作者单位：Dalhousie University; University of Sydney
摘要：We consider the first serial correlation coefficient under an AR(1) model where errors are not assumed to be Gaussian. In this case it is necessary to consider bootstrap approximations for tests based on the statistic since the distribution of errors is unknown. We obtain saddle-point approximations for tail probabilities of the statistic and its bootstrap version and use these to show that the bootstrap tail probabilities approximate the true values with given relative errors, thus extending ...
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作者：Jiang, Jiming
作者单位：University of California System; University of California Davis
摘要：We give answer to an open problem regarding consistency of the maximum likelihood estimators (MLEs) in generalized linear mixed models (GLMMs) involving crossed random effects. The solution to the open problem introduces an interesting, nonstandard approach to proving consistency of the MLEs in cases of dependent observations. Using the new technique, we extend the results to MLEs under a general GLMM. An example is used to further illustrate the technique.
