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作者：Hu, FF; Zhang, LX
作者单位：University of Virginia; Zhejiang University
摘要：A general doubly adaptive biased coin design is proposed for the allocation of subjects to K treatments in a clinical trial. This design follows the same spirit as Efron's biased coin design and applies to the cases where the desired allocation proportions are unknown, but estimated sequentially. Strong consistency, a law of the iterated logarithm and asymptotic normality of this design are obtained under some widely satisfied conditions. For two treatments, a new family of designs is proposed...
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作者：Berkes, I; Horváth, L
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Utah System of Higher Education; University of Utah
摘要：We propose a class of estimators for the parameters of a GARCH(p, q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maximum likelihood estimator based on exponential density performs better than the standard normal density...
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作者：Zhang, T
作者单位：International Business Machines (IBM); IBM USA
摘要：The discussants contributed different views on several aspects of large margin classification methods and outlined some interesting future directions. I would like to thank them for the stimulating comments. In the following I will mainly focus on two issues. One is the conditional probability modeling aspect of large margin classification methods and the other is related to properties of greedy algorithms used in boosting procedures.
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作者：Cai, TT; Low, MG
作者单位：University of Pennsylvania
摘要：A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds. In addition, minimax theory over nonconvex parameter spaces is developed.
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作者：Hall, P; Minnotte, MC; Zhang, CM
作者单位：Australian National University; Utah System of Higher Education; Utah State University; University of Wisconsin System; University of Wisconsin Madison
摘要：It is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a Gaussian density. There is numerical evidence of nonmonotonicity in the case of some non-Gaussian kernels, but little additional information is available. The present paper provides theoretical and numerical descriptions of the extent to which the number of modes is a nonmonotone function of bandwidth in the case of general compactly supported densities. Our res...
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作者：Walker, S
作者单位：University of Bath
摘要：We use martingales to study Bayesian consistency. We derive sufficient conditions for both Hettinger and Kullback-Leibler consistency, which do not rely on the use of a sieve. Alternative sufficient conditions for Hellinger consistency are also found and demonstrated on examples.
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作者：Grünwald, PD; Dawid, AP
作者单位：Centrum Wiskunde & Informatica (CWI); University of London; University College London
摘要：We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium theory of zero-sum games between Decision Maker and Nature, these two problems are shown to be dual to each other, the solution to each providing that to the other. Although Topsoe described this connection for the Shannon entropy over 20 years ago, it does ...
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作者：Loubes, JM; Massart, P
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
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作者：Beran, R
作者单位：University of California System; University of California Davis
摘要：This paper constructs improved estimators of the means in the Gaussian saturated one-way layout with an ordinal factor. The least squares estimator for the mean vector in this saturated model is usually inadmissible. The hybrid shrinkage estimators of this paper exploit the possibility of slow variation in the dependence of the means on the ordered factor levels but do not assume it and respond well to faster variation if present. To motivate the development, candidate penalized least squares ...
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作者：Douc, R; Moulines, T; Rydén, T
作者单位：IMT - Institut Mines-Telecom; IMT Atlantique; Lund University
摘要：An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution...
