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作者：Negahban, Sahand; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We study an instance of high-dimensional inference in which the goal is to estimate a matrix circle minus* is an element of R-m1xm2 on the basis of N noisy observations. The unknown matrix circle minus* is assumed to be either exactly low rank, or near low-rank, meaning that it can be well-approximated by a matrix with low rank. We consider a standard M-estimator based on regularization by the nuclear or trace norm over matrices, and analyze its performance under high-dimensional scaling. We d...
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作者：Cai, T. Tony; Low, Mark G.
作者单位：University of Pennsylvania
摘要：A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional 1/n Sigma vertical bar theta(i)vertical bar from an observation Y similar to N (theta, I-n). This problem exhibits some features that are significantly different from those that occur in estimating conventional smooth functionals. This is a setting where standard techniques fai...
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作者：Qian, Min; Murphy, Susan A.
作者单位：University of Michigan System; University of Michigan
摘要：Because many illnesses show heterogeneous response to treatment, there is increasing interest in individualizing treatment to patients [Arch. Gen. Psychiatry 66 (2009) 128-133]. An individualized treatment rule is a decision rule that recommends treatment according to patient characteristics. We consider the use of clinical trial data in the construction of an individualized treatment rule leading to highest mean response. This is a difficult computational problem because the objective functio...
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作者：Rohde, Angelika; Tsybakov, Alexandre B.
作者单位：University of Hamburg; Institut Polytechnique de Paris; ENSAE Paris
摘要：Suppose that we observe entries or, more generally, linear combinations of entries of an unknown m x T-matrix A corrupted by noise. We are particularly interested in the high-dimensional setting where the number mT of unknown entries can be much larger than the sample size N. Motivated by several applications, we consider estimation of matrix A under the assumption that it has small rank. This can be viewed as dimension reduction or sparsity assumption. In order to shrink toward a low-rank rep...
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作者：Belloni, Alexandre; Winkler, Robert L.
作者单位：Duke University
摘要：This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order perspective. We also study s...
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作者：Bunea, Florentina; She, Yiyuan; Wegkamp, Marten H.
作者单位：State University System of Florida; Florida State University
摘要：We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius norm of the fit plus a regularization term proportional to the number of parameters in the reduced rank model. The rank of the RSC estimator provides a consistent estimator of the rank of the coefficient matrix; in general, the rank of our estimator is a co...
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作者：Drton, Mathias; Foygel, Rina; Sullivant, Seth
作者单位：University of Chicago; North Carolina State University
摘要：Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms. We give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms. Global identifiability is understood to mean injectivity ...
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作者：Huckemann, Stephan F.
作者单位：University of Gottingen
摘要：For planar landmark based shapes, taking into account the non-Euclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised which rests on one of two asymptotic scenarios. For both scenarios, strong consistency and central limit theorems are established, along with an algorithm for the computation of a Ziezold mean geodesic. In application, this allows to verify the geodesic hypothesis for leaf growth of Canadian black poplars a...
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作者：Gao, Fuqing; Zhao, Xingqiu
作者单位：Wuhan University; Hong Kong Polytechnic University; Zhongnan University of Economics & Law
摘要：The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large deviations is proposed. The new method can be widely applied to driving the moderate deviations of estima...
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作者：Reiss, Markus
作者单位：Humboldt University of Berlin
摘要：We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function a and a nonstandard noise level. As an application, new rate-optimal estimators of the v...
