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作者：Friedlander, Michael P.; Saunders, Michael A.
作者单位：University of British Columbia; Stanford University
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作者：Buchmann, Borls; Chan, Ngai Hang
作者单位：Australian National University; Chinese University of Hong Kong
摘要：This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures converge to functionals of fractional Ornstein-Uhlenbeck processes. We use fractional integrated noise as an example to illustrate the important ideas. In this case, the functionals bear only formal analogy to those in the classical framework with uncorrelated...
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作者：Zhang, Li-Xin; Hu, Feifang; Cheung, Siu Hung; Chan, Wai Sum
作者单位：Zhejiang University; Chinese University of Hong Kong; University of Virginia; Chinese University of Hong Kong
摘要：Response-adaptive designs have been extensively studied and used in clinical trials. However, there is a lack of a comprehensive study of responseadaptive designs that include covariates, despite their importance in clinical trials. Because the allocation scheme and the estimation of parameters are affected by both the responses and the covariates, covariate-adjusted responseadaptive (CARA) designs are very complex to formulate. In this paper, we overcome the technical hurdles and lay out a fr...
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作者：Ghosal, Subhashis; Van Der Vaart, Aad
作者单位：North Carolina State University; Vrije Universiteit Amsterdam
摘要：We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent, nonidentically distributed observations, Markov processes, stationary Gaussian time series and the white noise model. We apply our general ...
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作者：Banerjee, Moulinath; Mckeague, Ian W.
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We investigate the problem of finding confidence sets for split points in decision trees (CART). Our main results establish the asymptotic distribution of the least squares estimators and some associated residual sum of squares statistics in a binary decision tree approximation to a smooth regression curve. Cube-root asymptotics with nonnormal limit distributions are involved. We study various confidence sets for the split point, one calibrated using the subsampling bootstrap, and others calib...
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作者：Zhu, Hongtu; Ibrahim, Joseph G.; Lee, Sikyum; Zhang, Heping
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill; Chinese University of Hong Kong; Yale University
摘要：Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133-169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative. The aim of this paper is to develop a diffe...
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作者：Lecue, Guillaume
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest an exponential weighting aggregation scheme. We use this aggregation procedure to construct classifiers which adapt automatically to margin and complexity. Two main examples are worked out in which adaptivity is achieved in frameworks proposed by Steinwart and Scovel [Learning Theory. Lecture Notes in Comput. Sci. 3559 (2005) 279-294. Springer, Berlin; Ann. Statist. 35 (2007) 575-607] and...
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作者：Tudor, Ciprian A.; Viens, Frederi G.
作者单位：heSam Universite; Universite Pantheon-Sorbonne; Purdue University System; Purdue University; Purdue University System; Purdue University
摘要：We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by a fractional Brownian motion with arty level of Holder-regularity (any Hurst parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We also pro...
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作者：Butucea, Cristina; Guta, Madalin; Artiles, Luis
作者单位：Universite Paris Nanterre; Utrecht University
摘要：We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum Systems. The state is represented through the Wigner function, a generalized probability density on R-2 which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The effect of the losses due to detection inefficiencies, which are always present in a real experiment, is the addition to the tomographic data of ind...
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作者：Hunter, David R.; Wang, Shaoli; Hettmansperger, Thomas P.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Yale University
摘要：This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no additional assumptions other than symmetry are made regarding the parametric form of the component distributions. Because the class of symmetric distributions is so broad, identifiability of parameters is a major issue in these mixtures. We develop a notion of...
