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作者：Han, Qiyang; Sen, Bodhisattva; Shen, Yandi
作者单位：Rutgers University System; Rutgers University New Brunswick; Columbia University; University of Washington; University of Washington Seattle
摘要：In the Gaussian sequence model Y = mu + xi, we study the likelihood ratio test (LRT) for testing H-0 : mu = mu(0) versus H-1 : mu is an element of K, where mu(0) is an element of K, and K is a closed convex set in R-n. In particular, we show that under the null hypothesis, normal approximation holds for the log-likelihood ratio statistic for a general pair (mu(0), K), in the high-dimensional regime where the estimation error of the associated least squares estimator diverges in an appropriate ...
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作者：Li, Bing; Song, Jun
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Korea University
摘要：We develop a general theory and estimation methods for functional linear sufficient dimension reduction, where both the predictor and the response can be random functions, or even vectors of functions. Unlike the existing dimension reduction methods, our approach does not rely on the estimation of conditional mean and conditional variance. Instead, it is based on a new statistical construction-the weak conditional expectation, which is based on Carleman operators and their inducing functions. ...
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作者：Pananjady, Ashwin; Samworth, Richard J.
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology; University of Cambridge
摘要：Motivated by models for multiway comparison data, we consider the problem of estimating a coordinatewise isotonic function on the domain [0, 1](d) from noisy observations collected on a uniform lattice, but where the design points have been permuted along each dimension. While the univariate and bivariate versions of this problem have received significant attention, our focus is on the multivariate case d >= 3. We study both the minimax risk of estimation (in empirical L-2 loss) and the fundam...
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作者：Beyhum, Jad; El Ghouch, Anouar; Portier, Francois; Van Keilegom, Ingrid
作者单位：KU Leuven; Universite Catholique Louvain; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Institut Polytechnique de Paris; ENSAE Paris
摘要：We consider the problem of estimating the distribution of time-to-event data that is subject to censoring and for which the event of interest might never occur, that is, some subjects are cured. To model this kind of data in the presence of covariates, one of the leading semiparametric models is the promotion time cure model (Stochastic Models of Tumor Latency and Their Biostatistical Applications (1996) World Scientific), which adapts the Cox model to the presence of cured subjects. Estimatin...
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作者：Kim, Ilmun; Balakrishnan, Sivaraman; Wasserman, Larry
作者单位：Yonsei University; Carnegie Mellon University
摘要：Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing popularity and empirical success, theoretical properties of the permutation test, especially its power, have not been fully explored beyond simple cases. In this paper, we attempt to partly fill this gap by presenting a general nonasymptotic framework for analyz...
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作者：Lahiry, Samriddha; Nussbaum, Michael
作者单位：Cornell University; Cornell University
摘要：In classical statistics, Pinsker's theorem provides an exact asymptotic minimax bound in nonparametric estimation, improving upon optimal rates of convergence results. We obtain a quantum version of the theorem by establishing asymptotic minimax results for estimation of the displacement vector in a quantum Gaussian white noise model, given by a sequence of shifted vacuum states. Analogous results are then obtained for estimation of a general pure state from an ensemble of identically prepared...
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作者：Chen, Yen-Chi
作者单位：University of Washington; University of Washington Seattle
摘要：We introduce the concept of pattern graphs-directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a missing not at random restriction. We introduce a selection model and a pattern mixture model formulations using the pattern graphs and show that they are equivalent. A pattern graph leads to an inverse probability weighting estimator as well as an imputation-base...
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作者：Spector, Asher; Janson, Lucas
作者单位：Harvard University
摘要：Model-X knockoffs (J. R. Stat. Soc. Ser. B. Stat. Methodol. 80 (2018) 551-577) allows analysts to perform feature selection using almost any machine learning algorithm while provably controlling the expected proportion of false discoveries. This procedure involves constructing synthetic variables, called knockoffs, which effectively act as controls during feature selection. The gold standard for constructing knockoffs has been to minimize the mean absolute correlation (MAC) between features an...
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作者：Luo, Yuetian; Zhang, Anru R.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Duke University
摘要：This paper studies the statistical and computational limits of high-order clustering with planted structures. We focus on two clustering models, constant high-order clustering (CHC) and rank-one higher-order clustering (ROHC), and study the methods and theory for testing whether a cluster exists (detection) and identifying the support of cluster (recovery). Specifically, we identify the sharp boundaries of signal-to-noise ratio for which CHC and ROHC detection/recovery are statistically possib...
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作者：Mukherjee, Gourab; Johnstone, Iain M.
作者单位：University of Southern California; Stanford University; Stanford University
摘要：We study predictive density estimation under Kullback-Leibler loss in l(0)-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. Fundamental for this is a new risk decomposition for sparse, or spike-and-slab priors. A surprise is the existence of a phase transition in the future-to-past variance ratio r. For r < r(0) = (root 5 - 1)/4, the natural discrete prior ceases to be asymptotically optimal. Instead, fo...
