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作者：Koul, Hira L.; Mueller, Ursula U.; Schick, Anton
作者单位：Michigan State University; Texas A&M University System; Texas A&M University College Station; State University of New York (SUNY) System; Binghamton University, SUNY
摘要：This paper gives a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed. This provides a convenient tool for obtaining the asymptotic behavior of complete case versions of established full data methods without lengthy proofs. The methodology is illustrated by analyzing three inference procedures for partially linear regression models with responses missing at random. We first ...
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作者：Kato, Kengo
作者单位：Hiroshima University
摘要：This paper studies estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for each fixed quantile index is modeled as a linear functional of the covariate. Here we suppose that covariates are discretely observed and sampling points may differ across subjects, where the number of measurements per subject increases as the sample size. Also, we allow the quantile index to vary over a given subse...
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作者：Xu, Ganggang; Huang, Jianhua Z.
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Although the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving the associated optimization problem is computationally expensive, especially when there are multiple tuning parameters. In this paper, by focusing on the penalized spline method, we show that the leave-subject-out CV is optimal in the sense that it is asympto...
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作者：Romano, Joseph P.; Shaikh, Azeem M.
作者单位：Stanford University; Stanford University; University of Chicago
摘要：This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions P. These results are then applied (i) to construct confidence regions that behave well uniformly over P in the sense that the coverage probability tends to at least the nominal level uniformly over P and (ii) to construct tests that behave well uniformly over P in the sense that...
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作者：Roman, Jorge Carlos; Hobert, James P.
作者单位：Vanderbilt University; State University System of Florida; University of Florida
摘要：Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple Gibbs sampler that can be employed to explore the posterior density. A popular default among the conditionally conjugate priors is an improper prior that takes a product form with a flat prior on the regression parameter, and so-called power priors on each of th...
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作者：Johnson, Leif T.; Geyer, Charles J.
作者单位：Alphabet Inc.; Google Incorporated; University of Minnesota System; University of Minnesota Twin Cities
摘要：A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian analysis with conjugate priors of logistic and Poisson regression and of log-linear models for categorical data result in posterior distributions that are not super-exponentially light. We show how to apply the change-of-variable formula for diffeomorphisms to ob...
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作者：Juditsky, Anatoli; Karzan, Fatma Kilinc; Nemirovski, Arkadi; Polyak, Boris
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Carnegie Mellon University; University System of Georgia; Georgia Institute of Technology; V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences; Russian Academy of Sciences
摘要：We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic noise, using block-l(1) regularization. While the current theory provides promising bounds for the recovery errors under a number of different, yet mostly hard to verify conditions, our emphasis is on verifiable conditions on the problem parameters (sensing matr...
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作者：Samworth, Richard J.; Yuan, Ming
作者单位：University of Cambridge; University System of Georgia; Georgia Institute of Technology
摘要：Independent Component Analysis (ICA) models are very popular semi-parametric models in which we observe independent copies of a random vector X = AS, where A is a non-singular matrix and S has independent components. We propose a new way of estimating the unmixing matrix W = A(-1) and the marginal distributions of the components of S using nonparametric maximum likelihood. Specifically, we study the projection of the empirical distribution onto the subset of ICA distributions having log-concav...
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作者：Belitser, Eduard; Ghosal, Subhashis; van Zanten, Harry
作者单位：Eindhoven University of Technology; North Carolina State University; University of Amsterdam
摘要：We propose a two-stage procedure for estimating the location mu and size M of the maximum of a smooth d-variate regression function f. In the first stage, a preliminary estimator of mu obtained from a standard nonparametric smoothing method is used. At the second stage, we zoom-in near the vicinity of the preliminary estimator and make further observations at some design points in that vicinity. We fit an appropriate polynomial regression model to estimate the location and size of the maximum....
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作者：Spokoiny, Vladimir
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Moscow Institute of Physics & Technology
摘要：The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not tend to infinity; (2) the parametric assumption is possibly misspecified and the underlying data distribution can lie beyond the given parametric family. These two features enable to bridge the gap between parametric and nonparametric theory and to build a uni...
