-
作者：Chen, Pinhan; Gao, Chao; Zhang, Anderson Y.
作者单位：University of Chicago; University of Pennsylvania
摘要：We consider the problem of ranking n players from partial pairwise comparison data under the Bradley-Terry-Luce model. For the first time in the literature, the minimax rate of this ranking problem is derived with respect to the Kendall's tau distance that measures the difference between two rank vectors by counting the number of inversions. The minimax rate of ranking exhibits a transition between an exponential rate and a polynomial rate depending on the magnitude of the signal-to-noise rati...
-
作者：Dette, Holger; Liu, Xin; Yue, Rong-Xian
作者单位：Ruhr University Bochum; Donghua University; Shanghai Normal University
摘要：The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of the optimization problem and have been successfully applied for models with univariate predictors. In particular, several authors have developed sufficient conditions for the existence of minimally supported designs in univariate models, where the number of s...
-
作者：Kou, Jiyao; Walther, Guenther
作者单位：Stanford University
摘要：The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing that is inherent in these problems. Here, we show that fundamentally more powerful statistical inference is possible when there is some structure in the signal that can be exploited, for example, if the signal is clustered in many small blocks,...
-
作者：Shao, Lingxuan; Lin, Zhenhua; Yao, Fang
作者单位：Peking University; National University of Singapore
摘要：A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from sparsely observed ...
-
作者：Zhao, Anqi; Lee, Youjin; Small, Dylan S.; Karmakar, Bikram
作者单位：National University of Singapore; Brown University; University of Pennsylvania; State University System of Florida; University of Florida
摘要：Valid instrumental variables enable treatment effect inference even when selection into treatment is biased by unobserved confounders. When multiple candidate instruments are available, but some of them are possibly invalid, the previously proposed reinforced design enables one or more nearly independent valid analyses that depend on very different assumptions. That is, we can perform evidence factor analysis. However, the validity of the reinforced design depends crucially on the order in whi...
-
作者：Chan, Kin Wai
作者单位：Chinese University of Hong Kong
摘要：Variance estimation is important for statistical inference. It becomes nontrivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or suboptimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with nonconstant means. The building blocks are difference statistics. The proposed class of estimators is general enough to cover many exis...
-
作者：He, Yuanzhen; Lin, C. Devon; Sun, Fasheng
作者单位：Beijing Normal University; Queens University - Canada; Northeast Normal University - China; Northeast Normal University - China
摘要：Orthogonal array, a classical and effective tool for collecting data, has been flourished with its applications in modern computer experiments and engineering statistics. Driven by the wide use of computer experiments with both qualitative and quantitative factors, multiple computer experiments, multifidelity computer experiments, cross-validation and stochastic optimization, orthogonal arrays with certain structures have been introduced. Sliced orthogonal arrays and nested orthogonal arrays a...
-
作者：Chen, Yaqing; Muller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：Local Frechet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy metric space valued random objects. We derive uniform rates of convergence, which so far have eluded theoretical analysis of this method, for both fixed and random target trajectories, where we utilize tools from empirical processes. These results are shown to ...
-
作者：Bykhovskaya, Anna; Gorin, Vadim
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：The paper analyzes cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, N, and the number of time periods, T, are large and of the same order. We propose a way to examine a VAR of order 1 for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from overrejection. This is a...
-
作者：Graczyk, Piotr; Ishi, Hideyuki; Kolodziejek, Bartosz; Massam, Helene
作者单位：Universite d'Angers; Osaka Metropolitan University; Warsaw University of Technology; York University - Canada
摘要：We consider multivariate centered Gaussian models for the random variable Z = (Z(1),..., Z(p)), invariant under the action of a subgroup of the group of permutations on {1,..., p}. Using the representation theory of the symmetric group on the field of reals, we derive the distribution of the maximum likelihood estimate of the covariance parameter Sigma and also the analytic expression of the normalizing constant of the Diaconis-Ylvisaker conjugate prior for the precision parameter K = Sigma(-1...
