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作者：Hu, Rui; Wiens, Douglas P.
作者单位：MacEwan University; University of Alberta
摘要：To aid in the discrimination between two, possibly nonlinear, regression models, we study the construction of experimental designs. Considering that each of these two models might be only approximately specified, robust maximin designs are proposed. The rough idea is as follows. We impose neighbourhood structures on each regression response, to describe the uncertainty in the specifications of the true underlying models. We determine the least favourable-in terms of Kullback-Leibler divergence...
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作者：Johndrow, James E.; Bhattacharya, Anirban; Dunson, David B.
作者单位：Duke University; Texas A&M University System; Texas A&M University College Station
摘要：Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support ...
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作者：Choi, Yunjin; Taylor, Jonathan; Tibshirani, Robert
作者单位：National University of Singapore; Stanford University; Stanford University
摘要：Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of principal components. In order to address this challenge, we propose distribution-based methods with exact type 1 error controls for hypothesis testing and construction of confidence intervals for signals in a noisy matrix with finite samples. Assuming Gaussian noise, we derive exact type 1 error controls based on the conditional distribution...
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作者：Constantinou, Panayiota; Dawid, A. Philip
作者单位：University of Warwick; University of Cambridge; University of Cambridge
摘要：The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions the calculus that applies for the two cases separately (axioms of a separoid) still applies for the extended case. These results provide a rigorous basis for a wide range of statistical concepts, including ancillarity and sufficiency, and, in particular, the D...
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作者：Feller, Chrystel; Schorning, Kirsten; Dette, Holger; Bermann, Georgina; Bornkamp, Bjoern
作者单位：Novartis; Ruhr University Bochum
摘要：A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in the administration frequency (but not in the sort of drug), a reasonable assumption is that the regression models for the different treatments share common parameters. This paper develops optimal design theory for the comparison of different regression models ...
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作者：Dicker, Lee H.; Erdogdu, Murat A.
作者单位：Rutgers University System; Rutgers University New Brunswick; Stanford University
摘要：We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models. Random-effects models and variance components estimation are classical topics in statistics, with a corresponding well-established asymptotic theory. However, our finite sample results for quadratic forms provide additional flexibility for easily analyzing rand...
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作者：Kong, Weihao; Valiant, Gregory
作者单位：Stanford University
摘要：We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the population spectrum), given access to samples drawn from the distribution. We consider this recovery problem in the regime where the sample size is comparable to, or even sublinear in the dimensionality of the distribution. First, we propose a theoretically optimal and computationally efficient algorithm for recovering the momen...
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作者：Han, Dong; Tsung, Fugee; Xian, Jinguo
作者单位：Shanghai Jiao Tong University; Hong Kong University of Science & Technology
摘要：By introducing suitable loss random variables of detection, we obtain optimal tests in terms of the stopping time or alarm time for Bayesian changepoint detection not only for a general prior distribution of change-points but also for observations being a Markov process. Moreover, the optimal (minimal) average detection delay is proved to be equal to 1 for any (possibly large) average run length to false alarm if the number of possible change-points is finite.
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作者：Kong, Yinfei; Li, Daoji; Fan, Yingying; Lv, Jinchi
作者单位：California State University System; California State University Fullerton; State University System of Florida; University of Central Florida; University of Southern California
摘要：Feature interactions can contribute to a large proportion of variation in many prediction models. In the era of big data, the coexistence of high dimensionality in both responses and covariates poses unprecedented challenges in identifying important interactions. In this paper, we suggest a two-stage interaction identification method, called the interaction pursuit via distance correlation (IPDC), in the setting of high-dimensional multi-response interaction models that exploits feature screen...
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作者：Chernozhukov, Victor; Galichon, Alfred; Hallin, Marc; Henry, Marc
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); New York University; New York University; Institut d'Etudes Politiques Paris (Sciences Po); Universite Libre de Bruxelles; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks and signs, based on canonical transportation maps between a distribution of interest on R-d and a reference distribution on the d-dimensional unit ball. The new depth concept, called Monge Kantorovich depth, specializes to halfspace depth for d = 1 and in the case of spherical distributions, but for more general distributions, differs from the latter in the ability for its contours to accoun...
