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作者：Banerjee, Moulinath
作者单位：University of Michigan System; University of Michigan
摘要：The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the usual parametric or semiparametric situations in that the MLE of the monotone function at a point converges to the truth at rate n(1/3) (slower than the usual root n rate) with a non-Gaussian limit distribution. A framework for likelihood based estimation o...
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作者：Ing, Ching-Kang
作者单位：Academia Sinica - Taiwan; National Taiwan University
摘要：The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APES,, is investigated in infinite-order autoregressive (AR(infinity)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APES, is obtained by summing these squared errors from stage n delta(n), where n is the sample size and 1/n <= delta(n) <= 1 - (1/1n) may depend on n. Under certain regularity conditions, an asymptotic expression is derived for the...
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作者：Ling, Shiqing
作者单位：Hong Kong University of Science & Technology
摘要：This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald test for change points in a general class of time series models under the no change-point hypothesis. As an application, we verify our assumptions for the long-memory fractional ARIMA model.
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作者：Durot, Cecile
作者单位：Universite Paris Saclay
摘要：We aim at estimating a function lambda : [0, 1] -> R, subject to the constraint that it is decreasing (or increasing). We provide a unified approach for studying the L-p-loss of an estimator defined as the slope of a concave (or convex) approximation of an estimator of a primitive of., based on n observations. Our main task is to prove that the Lp-loss is asymptotically Gaussian with explicit (though unknown) asymptotic mean and variance. We also prove that the local L-p-risk at a fixed point ...
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作者：Gine, Evarist; Mason, David M.
作者单位：University of Connecticut; University of Delaware
摘要：A notion of local U-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U-processes that may be useful in other contexts. This local U-statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer Statist. Assoc. 89 (1994) 517-525] and, as a consequence, uniform in bandwidth central limit theorems in the sup and in the L-p norms...
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作者：Zhang, Jin-Ting; Chen, Jianwei
作者单位：National University of Singapore; California State University System; San Diego State University; University of Rochester
摘要：With modem technology development, functional data are being observed frequently in many scientific fields. A popular method for analyzing such functional data is '' smoothing first, then estimation.'' That is, statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another. However, little is known about this substitution e...
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作者：Cuevas, Antonio; Fraiman, Ricardo; Rodriguez-Casal, Alberto
作者单位：Autonomous University of Madrid; Universidade de Santiago de Compostela
摘要：The Minkowski content L-0(G) of a body G C R-d represents the bound ary length (for d = 2) or the surface area (for d = 3) of G. A method for estimating L-0(G) is proposed. It relies on a nonparametric estimator based on the information provided by a random sample (taken on a rectangle containing G) in which we are able to identify whether every point is inside or outside G. Some theoretical properties concerning strong consistency, L-1-error and convergence rates are obtained. A practical app...
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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：Letac, Gerard; Massam, Helene
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; York University - Canada
摘要：When considering a graphical Gaussian model N-G Markov with respect to a decomposable graph G, the parameter space of interest for the precision parameter is the cone PG of positive definite matrices with fixed zeros corresponding to the missing edges of G. The parameter space for the scale parameter of N-G is the cone Q(G), dual to P-G, of incomplete matrices with submatrices corresponding to the cliques of G being positive definite. In this paper we construct on the cones Q(G) and P-G two fa...
