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作者：van der Laan, MJ; McKeague, IW
作者单位：University of California System; University of California Berkeley; State University System of Florida; Florida State University
摘要：The Kaplan-Meier estimator of a survival function is well known to be asymptotically efficient when cause of failure is always observed. It has been an open problem, however, to find an efficient estimator when failure indicators are missing at random. Lo showed that nonparametric maximum likelihood estimators are inconsistent, and this has led to several proposals of ad hoc estimators, none of which are efficient. We now introduce a sieved nonparametric maximum likelihood estimator, and show ...
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作者：Diaconis, P; Sturmfels, B
作者单位：Cornell University; University of California System; University of California Berkeley
摘要：We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include contingency tables, logistic regression, and spectral analysis of permutation data. The algorithms involve computations in polynomial rings using Grobner bases.
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作者：Girard, DA
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：When using nonparametric estimates of the mean curve, surface or image underlying noisy observations, the selection of smoothing parameters is generally crucial. This paper gives a theoretical comparison of the performances of generalized cross-validation (GCV) and of its fast randomized version (RGCV), as selection criteria. This is mainly done by studying the asymptotic distribution of the excess error for each selector, that is, the difference between the (data-driven) resulting average squ...
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作者：Mallat, S; Papanicolaou, G; Zhang, ZF
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Stanford University
摘要：It is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. We model locally stationary processes with pseudo-differential operators that are time-varying convolutions. An adaptive covariance estimation is calculated by searching first for a best local cosine basis which approximates the covariance by a band or a diagonal matrix. The estimation is obtained from regularized versions of the diagonal coefficients in the be...
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作者：Brooks, SP
作者单位：University of Bristol
摘要：We begin by showing how piecewise linear bounds may be devised, which bound both above and below any concave log-density in general dimensions. We then show how these bounds may be used to gain an upper bound to the volume in the tails outside the convex hull of the sample path in order to assess how well the sampler has explored the target distribution. This method can be used as a stand-alone diagnostic to determine when the sampler output provides a reliable basis for inference on the stati...
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作者：Efromovich, S
作者单位：University of New Mexico
摘要：A data-driven estimate is given that, over a Sobolev space, is simultaneously asymptotically sharp minimax for estimating both the function and its derivatives under integrated squared error loss. It is also shown that linear estimates cannot be simultaneously asymptotically sharp minimax over a given Sobolev space.
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作者：Drees, H
作者单位：University of Cologne
摘要：Hall and Welsh established the best attainable rate of convergence for estimates of a positive extreme value index gamma under a certain second order condition implying that the distribution function of the maximum of n random variables converges at an algebraic rate to the pertaining extreme value distribution. As a first generalization, we obtain a surprisingly sharp bound on the estimation error if gamma is still assumed to be positive, but the rate of convergence of the maximum may be nona...
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作者：Huang, JHZ
作者单位：University of Pennsylvania; University of California System; University of California Berkeley
摘要：A general theory on rates of convergence of the least-squares projection estimate in multiple regression is developed. The theory is applied to the functional ANOVA model, where the multivariate regression function is modeled as a specified sum of a constant term, main effects (functions of one variable) and selected interaction terms (functions of two or more variables). The least-squares projection is onto an approximating space constructed from arbitrary linear spaces of functions and their...
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作者：Nielsen, JP; Linton, O; Bickel, PJ
作者单位：Yale University; University of California System; University of California Berkeley
摘要：A semiparametric hazard model with parametrized time but general covariate dependency is formulated and analyzed inside the framework of counting process theory. A profile likelihood principle is introduced for estimation of the parameters: the resulting estimator is n(1/2)-consistent, asymptotically normal and achieves the semiparametric efficiency bound. An estimation procedure for the nonparametric part is also given and its asymptotic properties are derived. We provide an application to mo...
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作者：Parner, E
作者单位：Aarhus University
摘要：The frailty model is a generalization of Cox's proportional hazard model, where a shared unobserved quantity in the intensity induces a positive correlation among the survival times. Murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator (NPMLE) for the shared gamma-frailty model without covariates. In this paper we extend this result to the correlated gamma-frailty model, and we allow for covariates. We discuss the definition of the nonparametric ...
