-
作者：Asgharian, Masoud; Carone, Marco; Fakoor, Vahid
作者单位：McGill University; University of California System; University of California Berkeley; Ferdowsi University Mashhad
摘要：The multiplicative censoring model introduced in Vardi [Biometrika 76 (1989) 751-761] is an incomplete data problem whereby two independent samples from the lifetime distribution G, X-m = (X-1, ... , X-m) and Z(n) = (Z(1), ... , Z(n)), are observed subject to a form of coarsening. Specifically, sample X-m is fully observed while Y-n = (Y-1, ... , Y-n) is observed instead of Z(n), where Y-i = U(i)Z(i) and (U-1, ... , U-n) is an independent sample from the standard uniform distribution. Vardi [B...
-
作者：Cook, R. Dennis; Forzani, Liliana; Rothman, Adam J.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); National University of the Littoral
摘要：We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are consistent in a variety of settings, particularly in abundant regressions where most predictors contribute some information on the response, and oracle rates are possible. Simulation results are presented to support the theoretical conclusion.
-
作者：Uhler, Caroline
作者单位：Institute of Science & Technology - Austria
摘要：We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum likelihood estimator (MLE) exists with probability one. This is applied to bipartite graphs, grids and colored graphs. We also study the ML degree, and we present the first instance of a graph for which the MLE exists with probability one, even when the number o...
-
作者：Xia, Han; Wu, Wei Biao
作者单位：University of Chicago
摘要：We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351-376] idea and relate eigenvalues of covariance matrices to the spectral densities or Fourier transforms ...
-
作者：Parry, Matthew; Dawid, A. Philip; Lauritzen, Steffen
作者单位：University of Otago; University of Cambridge; University of Oxford
摘要：We investigate proper scoring rules for continuous distributions on the real line. It is known that the log score is the only such rule that depends on the quoted density only through its value at the outcome that materializes. Here we allow further dependence on a finite number in of derivatives of the density at the outcome, and describe a large class of such m-local proper scoring rules: these exist for all even m but no odd m. We further show that for m >= 2 all such m-local rules can be c...
-
作者：Delaigle, Aurore; Hall, Peter
作者单位：University of Melbourne
摘要：We introduce new nonparametric predictors for homogeneous pooled data in the context of group testing for rare abnormalities and show that they achieve optimal rates of convergence. In particular, when the level of pooling is moderate, then despite the cost savings, the method enjoys the same convergence rate as in the case of no pooling. In the setting of over-pooling the convergence rate differs from that of an optimal estimator by no more than a logarithmic factor. Our approach improves on ...
-
作者：Dawid, Philip; Lauritzen, Steffen; Parry, Matthew
作者单位：University of Cambridge; University of Oxford; University of Otago
摘要：A scoring rule is a loss function measuring the quality of a quoted probability distribution Q for a random variable X, in the light of the realized outcome x of X; it is proper if the expected score, under any distribution P for X, is minimized by quoting Q = P. Using the fact that any differentiable proper scoring rule on a finite sample space X is the gradient of a concave homogeneous function, we consider when such a rule can be local in the sense of depending only on the probabilities quo...
-
作者：Jirak, Moritz
作者单位：Graz University of Technology
摘要：Let {X-k, k is an element of Z} be an autoregressive process of order q. Various estimators for the order q and the parameters Theta(q) = (theta(1), ... , theta(q))(T) are known; the order is usually determined with Akaike's criterion or related modifications, whereas Yule-Walker, Burger or maximum likelihood estimators are used for the parameters Theta(q). In this paper, we establish simultaneous confidence bands for the Yule-Walker estimators (theta) over cap (i); more precisely, it is shown...
-
作者：Plamadeala, Victoria; Rosenberger, William F.
作者单位：George Mason University
摘要：Sequential monitoring in clinical trials is often employed to allow for early stopping and other interim decisions, while maintaining the type I error rate. However, sequential monitoring is typically described only in the context of a population model. We describe a computational method to implement sequential monitoring in a randomization-based context. In particular, we discuss a new technique for the computation of approximate conditional tests following restricted randomization procedures...
-
作者：Chen, Dong; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which ...
