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作者：Bai, Shuyang; Taqqu, Murad S.
作者单位：University System of Georgia; University of Georgia; Boston University
摘要：For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However, due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to establish the asymptotic...
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作者：Tang, Chuan-Fa; Wang, Dewei; Tebbs, Joshua M.
作者单位：University of South Carolina System; University of South Carolina Columbia
摘要：We propose L-p distance-based goodness-of-fit (GOF) tests for uniform stochastic ordering with two continuous distributions F and G, both of which are unknown. Our tests are motivated by the fact that when F and G are uniformly stochastically ordered, the ordinal dominance curve R = FG(-1) is star-shaped. We derive asymptotic distributions and prove that our testing procedure has a unique least favorable configuration of F and G for p is an element of [1, infinity]. We use simulation to assess...
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作者：Loh, Po-Ling; Wainwright, Martin J.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We develop a new primal-dual witness proof framework that may be used to establish variable selection consistency and l(infinity)-bounds for sparse regression problems, even when the loss function and regularizer are nonconvex. We use this method to prove two theorems concerning support recovery and l(infinity)-guarantees for a regression estimator in a general setting. Notably, our theory applies to all potential stationary points of the objective and certifies that the stationary point is un...
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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：Chambaz, Antoine; Zheng, Wenjing; van der Laan, Mark J.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：This article studies the targeted sequential inference of an optimal treatment rule (TR) and its mean reward in the nonexceptional case, that is, assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adapti...
