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作者：Uhler, Caroline
作者单位：Institute of Science & Technology - Austria
摘要：We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum likelihood estimator (MLE) exists with probability one. This is applied to bipartite graphs, grids and colored graphs. We also study the ML degree, and we present the first instance of a graph for which the MLE exists with probability one, even when the number o...
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作者：Lauritzen, Steffen; Meinshausen, Nicolai
作者单位：University of Oxford
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作者：Xia, Han; Wu, Wei Biao
作者单位：University of Chicago
摘要：We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351-376] idea and relate eigenvalues of covariance matrices to the spectral densities or Fourier transforms ...
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作者：Mammen, Enno; Rothe, Christoph; Schienle, Melanie
作者单位：University of Mannheim; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Humboldt University of Berlin
摘要：We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous applications, including two-stage nonparametric regression, estimation of simultaneous equation models or censored regression models. Yet so far there seems to be no general theory for their impact on the final estimator's statistical properties. Our paper p...
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作者：Rigollet, Philippe
作者单位：Princeton University
摘要：In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the parameter or even that the model on the systematic component is true. It is shown that this problem can be solved by constrained and/or penalized likelihood maximization and we deri...
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作者：Samworth, Richard J.
作者单位：University of Cambridge
摘要：We derive an asymptotic expansion for the excess risk (regret) of a weighted nearest-neighbour classifier. This allows us to find the asymptotically optimal vector of nonnegative weights, which has a rather simple form. We show that the ratio of the regret of this classifier to that of an unweighted k-nearest neighbour classifier depends asymptotically only on the dimension d of the feature vectors, and not on the underlying populations. The improvement is greatest when d = 4, but thereafter d...
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作者：Fellouris, Georgios
作者单位：University of Southern California
摘要：A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear with respect to a common parameter. A novel estimating scheme is suggested, according to which each sensor transmits only one-bit messages at stopping times of its local filtration. The proposed estimator is shown to be consistent and, for a large class of proc...
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作者：Ingster, Yuri I.; Sapatinas, Theofanis; Suslina, Irina A.
作者单位：Saint Petersburg State Electrotechnical University; University of Cyprus; ITMO University
摘要：Ill-posed inverse problems arise in various scientific fields. We consider the signal detection problem for mildly, severely and extremely ill-posed inverse problems with l(q)-ellipsoids (bodies), q is an element of (0, 2], for Sobolev, analytic and generalized analytic classes of functions under the Gaussian white noise model. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are, often, nonadaptive. Minimax rate-opti...
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作者：Loh, Po-Ling; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley
摘要：Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these issues in the context of high-dimensional sparse linear regression, and propose novel estimators for the cases of noisy, missing and/or dependent data. Many standard approaches to noisy or missing data, such as those using the EM algorithm, lead to optimization p...
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作者：Zhang, Ting; Wu, Wei Biao
作者单位：University of Iowa; University of Chicago
摘要：We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a n(1/2)-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion ...
