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作者：Wang, Tengyao; Berthet, Quentin; Samworth, Richard J.
作者单位：University of Cambridge; California Institute of Technology
摘要：extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse. An impressive range of estimators have been proposed; some of these are fast to compute, while others are known to achieve the mini-max optimal rate over certain Gaussian or sub-Gaussian classes. In this paper, we show that, under a widely-believe...
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作者：Cheng, Ming-Yen; Honda, Toshio; Li, Jialiang
作者单位：National Taiwan University; Hitotsubashi University; National University of Singapore
摘要：In semivarying coefficient modeling of longitudinal/clustered data, of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression using the true within-subject covariance matrices, which are often unavailable in reality. Thus, we propose an estimator when the covariance matrices are unknown and depend onl...
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作者：Cavaliere, Giuseppe; Georgiev, Iliyan; Taylor, A. M. Robert
作者单位：University of Bologna; Universidade Nova de Lisboa; University of Essex
摘要：We extend the available asymptotic theory for autoregressive sieve estimators to cover the case of stationary and invertible linear processes driven by independent identically distributed (i.i.d.) infinite variance (IV) innovations. We show that the ordinary least squares sieve estimates, together with estimates of the impulse responses derived from these, obtained from an autoregression whose order is an increasing function of the sample size, are consistent and exhibit asymptotic properties ...
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作者：Liu, Hongcheng; Yao, Tao; Li, Runze
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, they lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facilitates us in developing mixed integer linear programming reformulations, which admit finite algorithms ...
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作者：Cai, T. Tony; Zhang, Linjun
作者单位：University of Pennsylvania
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作者：Kim, Yongdai; Jeon, Jong-June
作者单位：Seoul National University (SNU); University of Seoul
摘要：In this paper, we study asymptotic properties of model selection criteria for high-dimensional regression models where the number of covariates is much larger than the sample size. In particular, we consider a class of loss functions calIed the class of quadratically supported risks which is large enough to include the quadratic loss, Huber loss, quantile loss and logistic loss. We provide sufficient conditions for the model selection criteria, which are applicable to the class of quadraticall...
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作者：Paul, Debashis; Peng, Jie; Burman, Prabir
作者单位：University of California System; University of California Davis
摘要：We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity conditions, we show that in terms of L-2-loss, the optimal rate of convergence for the proposed estimator is the same as that for the estimation of the derivative of a function. We conduct simulation studies to examine the finite sample behavior of the proposed estim...
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作者：Fan, Yingying; Lv, Jinchi
作者单位：University of Southern California
摘要：Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient estimation (ISEE) for estimating large precision matrix. Motivated by the innovated transformation, we convert the original problem into that of large covariance matrix estimation. The suggested method combines the strengths of recent advances in high-dimensional ...
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作者：Hsing, Tailen; Brown, Thomas; Thelen, Brian
作者单位：University of Michigan System; University of Michigan; Exponent
摘要：Dense spatial data are commonplace nowadays, and they provide the impetus for addressing nonstationarity in a general way. This paper extends the notion of intrinsic random function by allowing the stationary component of the covariance to vary with spatial location. A nonparametric estimation procedure based on gridded data is introduced for the case where the covariance function is regularly varying at any location. An asymptotic theory is developed for the procedure on a fixed domain by let...
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作者：Lei, Huang; Xia, Yingcun; Qin, Xu
作者单位：Southwest Jiaotong University; National University of Singapore; University of Electronic Science & Technology of China
摘要：Serial correlation in the residuals of time series models can cause bias in both model estimation and prediction. However, models with such serially correlated residuals are difficult to estimate, especially when the regression function is nonlinear. Existing estimation methods require strong assumption for the relation between the residuals and the regressors, which excludes the commonly used autoregressive models in time series analysis. By extending the Whittle likelihood estimation, this p...
