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作者：Agarwal, Alekh; Negahban, Sahand; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：Many statistical M-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite gradient methods for solving such problems, working within a high-dimensional framework that allows the ambient dimension d to grow with (and possibly exceed) the sample size n. Our theory identifies conditions under which projected gradient descent enjoys globally ...
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作者：Durot, Cecile; Kulikov, Vladimir N.; Lopuhaa, Hendrik P.
作者单位：Delft University of Technology
摘要：Let f be a nonincreasing function defined on [0, 1]. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between f and its Grenander-type estimator on sub-intervals of [0, 1]. The rate of convergence is found to be of order (n/logn)(-1/3) and the limiting distribution to be Gumbel.
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作者：Todorov, Viktor; Tauchen, George
作者单位：Northwestern University; Duke University
摘要：We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable Levy densities in the setting where both the time span of the data set increases, and the mesh of the observation grid decreases. The estimation is based on constructing a nonparametric estimate for the empirical Laplace transform of the stochastic scale over a given interval of time by aggregating high-frequency increments of the observed process on that time i...
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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...
