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作者：Liang, Hua; Liu, Xiang; Li, Runze; Tsai, Chih-Ling
作者单位：University of Rochester; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of California System; University of California Davis
摘要：In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously select variables and estimate regression coefficients. We show that the resulting SCAD estimators are consistent and possess the oracle property. Subsequently, we demonstrate that a proposed tuning parameter selector, BIC, identifies the true model consist...
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作者：Addario-Berry, Louigi; Broutin, Nicolas; Devroye, Luc; Lugosi, Gabor
作者单位：McGill University; McGill University; ICREA; Pompeu Fabra University; McGill University
摘要：We study a class of hypothesis testing problems in which, upon observing the realization of an n-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether there is a subset of the components belonging to a certain given class of sets whose elements have been contaminated, that is, have a mean different from zero. We establish some general conditions under which testing is possible and others under which testing is...
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作者：Brien, C. J.; Bailey, R. A.
作者单位：University of South Australia; University of London; Queen Mary University London
摘要：We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that...
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作者：Huang, Junzhou; Zhang, Tong
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.
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作者：Xue, Hongqi; Miao, Hongyu; Wu, Hulin
作者单位：University of Rochester
摘要：This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge-Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical error and measurem...
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作者：Delaigle, Aurore; Hall, Peter
作者单位：University of Melbourne; University of Bristol; University of California System; University of California San Diego
摘要：The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the notion of density when functional data are considered in the space determined by the eigenfunctions of principal component analysis. This leads to a transparent and meaningful surrogate for density defined in terms of the average value of the logarithms of t...
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作者：Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We propose MC+, a fast, continuous, nearly unbiased and accurate method of penalized variable selection in high-dimensional linear regression. The LASSO is fast and continuous, but biased. The bias of the LASSO may prevent consistent variable selection. Subset selection is unbiased but computationally costly. The MC+ has two elements: a minimax concave penalty (MCP) and a penalized linear unbiased selection (PLUS) algorithm. The MCP provides the convexity of the penalized loss in sparse region...
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作者：Klemela, Jussi; Mammen, Enno
作者单位：University of Oulu; University of Mannheim
摘要：We study estimation of a multivariate function f : R-d -> R when the observations are available from the function Af. where A is a known linear operator. Both the Gaussian white noise model and density estimation are studied. We define an L-2-empirical risk functional which is used to define a delta-net minimizer and a dense empirical risk minimizer. Upper bounds for the mean integrated squared error of the estimators are given. The upper bounds show how the difficulty of the estimation depend...
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作者：Chan, Ngai Hang; Ling, Shiqing
作者单位：Chinese University of Hong Kong; Hong Kong University of Science & Technology
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作者：Lang, Faming
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems a...
