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作者：Bartroff, Jay
作者单位：University of Southern California
摘要：A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling costs and error probabilities, these tests are shown to minimize the integrated risk to second order as the costs per stage and per observation approach zero. A numerical study shows significant improvement over group sequential tests in a binomial testing problem.
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作者：Li, Yehua; Wang, Naisyin; Hong, Meeyoung; Turner, Nancy D.; Lupton, Joanne R.; Carroll, Raymond J.
作者单位：University System of Georgia; University of Georgia; Texas A&M University System; Texas A&M University College Station; Texas A&M University System; Texas A&M University College Station
摘要：In longitudinal and spatial studies, observations often demonstrate strong correlations that are stationary in time or distance lags, and the times or locations of these data being sampled may not be homogeneous. We propose a nonparametric estimator of the correlation function in such data, using kernel methods. We develop a pointwise asymptotic normal distribution for the proposed estimator, when the number of subjects is fixed and the number of vectors or functions within each subject goes t...
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作者：Low, Mark G.; Zhou, Harrison H.
作者单位：University of Pennsylvania; Yale University
摘要：This paper examines asymptotic equivalence in the sense of Le Cam between density estimation experiments and the accompanying Poisson experiments. The significance of asymptotic equivalence is that all asymptotically optimal statistical procedures can be carried over from one experiment to the other. The equivalence given here is established under a weak assumption on the parameter space T. In particular, a sharp Besov smoothness condition is given on T which is sufficient for Poissonization, ...
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作者：Rosset, Saharon; Zhu, Ji
作者单位：International Business Machines (IBM); IBM USA; University of Michigan System; University of Michigan
摘要：We consider the generic regularized optimization problem (beta) over cap(lambda) = arg min(beta) L (y, X beta) + lambda J (beta). Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407-499] have shown that for the LASSO-that is, if L is squared error loss and J(beta) = vertical bar vertical bar beta vertical bar vertical bar(1) is the if l(1) norm of beta-the optimal coefficient path is piecewise linear, that is, is piecewise constant. We derive a general characterization of the ...
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作者：Yang, Yuhong
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Theoretical developments on cross validation (CV) have mainly focused on selecting one among a list of finite-dimensional models (e.g., subset or order selection in linear regression) or selecting a smoothing parameter (e.g., bandwidth for kernel smoothing). However, little is known about consistency of cross validation when applied to compare between parametric and nonparametric methods or within nonparametric methods. We show that under some conditions, with an appropriate choice of data spl...
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作者：Brown, Lawrence D.; Levine, M.
作者单位：University of Pennsylvania; Purdue University System; Purdue University
摘要：Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for suitable asymptotic formulations our estimators achieve the minimax rate.
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作者：Wang, Haonan; Marron, J. S.
作者单位：Colorado State University System; Colorado State University Fort Collins; University of North Carolina; University of North Carolina Chapel Hill
摘要：Object oriented data analysis is the statistical analysis of populations of complex objects. In the special case of functional data analysis, these data objects are curves, where standard Euclidean approaches, such as principal component analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non-Euclidean spaces, such as Lie groups and symmetric spaces, or of s...
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作者：Chan, Hock Peng; Fuh, Cheng-Der; Hu, Inchi
作者单位：National University of Singapore; National Central University; Hong Kong University of Science & Technology
摘要：Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each phase, one can pursue the projects in any order. When pursuing the project with one unit of resource, the project state changes according to a Markov chain. The probability distribution of the Markov chain is known up to an unknown parameter. When pursued, ...
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作者：Mokkadem, Abdelkader; Pelletier, Mariane
作者单位：Universite Paris Saclay
摘要：A stochastic algorithm for the recursive approximation of the location theta of a maximum of a regression function was introduced by Kiefer and Wolfowitz [Ann. Math. Statist. 23 (1952) 462-466] in the univariate framework, and by Blum [Ann. Math. Statist. 25 (1954) 737-744] in the multivariate case. The aim of this paper is to provide a companion algorithm to the Kiefer-Wolfowitz-Blum algorithm, which allows one to simultaneously recursively approximate the size p of the maximum of the regress...
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作者：Olshen, Richard A.
作者单位：Stanford University
摘要：This paper provides answers to questions regarding the almost sure limiting behavior of rooted, binary tree-structured rules for regression. Examples show that questions raised by Gordon and Olshen in 1984 have negative answers. For these examples of regression functions and sequences of their associated binary tree-structured approximations, for all regression functions except those in a set of the first category, almost sure consistency fails dramatically on events of full probability. One c...
