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作者：Zhu, Ke; Ling, Shiqing
作者单位：Hong Kong University of Science & Technology
摘要：This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA-GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A sim...
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作者：Lounici, Karim; Pontil, Massimiliano; van de Geer, Sara; Tsybakov, Alexandre B.
作者单位：University System of Georgia; Georgia Institute of Technology; University of London; University College London; Swiss Federal Institutes of Technology Domain; ETH Zurich; Institut Polytechnique de Paris; ENSAE Paris
摘要：We consider the problem of estimating a sparse linear regression vector beta* under a Gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern, namely the set of variables is partitioned into prescribed groups, only few of which are relevant in the estimation process. This group sparsity assumption suggests us to consider the Group Lasso method as a means to estimate beta*. We establish oracle inequalities...
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作者：Wang, Li; Liu, Xiang; Liang, Hua; Carroll, Raymond J.
作者单位：University System of Georgia; University of Georgia; University of Rochester; Texas A&M University System; Texas A&M University College Station
摘要：We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection proced...
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作者：Zhang, Chunming; Fan, Jianqing; Yu, Tao
作者单位：University of Wisconsin System; University of Wisconsin Madison; Princeton University; National University of Singapore
摘要：The multiple testing procedure plays an important role in detecting the presence of spatial signals for large-scale imaging data. Typically, the spatial signals are sparse but clustered. This paper provides empirical evidence that for a range of commonly used control levels, the conventional FDR procedure can lack the ability to detect statistical significance, even if the p-values under the true null hypotheses are independent and uniformly distributed; more generally, ignoring the neighborin...
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作者：Yin, Xiangrong; Li, Bing
作者单位：University System of Georgia; University of Georgia; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box-Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible and easy to implemen...
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作者：Bacallado, Sergio
作者单位：Stanford University
摘要：We define a conjugate prior for the reversible Markov chain of order r. The prior arises from a partially exchangeable reinforced random walk, in the same way that the Beta distribution arises from the exchangeable Polya urn. An extension to variable-order Markov chains is also derived. We show the utility of this prior in testing the order and estimating the parameters of a reversible Markov model.
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作者：Chi, Zhiyi
作者单位：University of Connecticut
摘要：The performance of multiple hypothesis testing is known to be affected by the statistical dependence among random variables involved. The mechanisms responsible for this, however, are not well understood. We study the effects of the dependence structure of a finite state hidden Markov model (HMM) on the likelihood ratios critical for optimal multiple testing on the hidden states. Various convergence results are obtained for the likelihood ratios as the observations of the HMM form an increasin...
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作者：Gine, Evarist; Nickl, Richard
作者单位：University of Connecticut; University of Cambridge
摘要：The frequentist behavior of nonparametric Bayes estimates, more specifically, rates of contraction of the posterior distributions to shrinking L-r-norm neighborhoods, 1 <= r <= infinity, of the unknown parameter, are studied. A theorem for nonparametric density estimation is proved under general approximation-theoretic assumptions on the prior. The result is applied to a variety of common examples, including Gaussian process, wavelet series, normal mixture and histogram priors. The rates of co...
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作者：Buhlmann, Peter; Cai, Tony
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Pennsylvania
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作者：Lerman, Gilad; Zhang, Teng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We assume i.i.d. data sampled from a mixture distribution with K components along fixed d-dimensional linear subspaces and an additional outlier component. For p > 0, we study the simultaneous recovery of the K fixed subspaces by minimizing the l(p)-averaged distances of the sampled data points from any K subspaces. Under some conditions, we show that if 0 < p <= 1, then all underlying subspaces can be precisely recovered by l(p) minimization with overwhelming probability. On the other hand, i...
