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作者：Spokoiny, Vladimir; Vial, Celine
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
摘要：This paper discusses the problem of adaptive estimation Of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from Lepski [Theory Probab. Appl. 35 (1990) 454-466.] that selects in a data-driven way one estimate Out of a given class of estimates ordered by their variability. A serious problem with using this and similar procedures is the choice of some tuning parameters lik...
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作者：Jiang, Wenhua; Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions on the unknown means, the average mean squared error (MSE) of the GMLEB is within an infinitesimal fraction of the minimum average MSE among all separable estimators which use a single deterministic estimating function on individual observations, provided that the risk is of greater order than (log...
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作者：Zou, Hui; Zhang, Hao Helen
作者单位：University of Minnesota System; University of Minnesota Twin Cities; North Carolina State University
摘要：We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J Amer. Statist. Assoc. 96 (2001) 1348-1360] and [Ann. Statist. 32 (2004) 928-961] which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem, which should be properly handled by the ideal method. Many existing variabl...
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作者：Wang, Huixia Judy; Fygenson, Mendel
作者单位：North Carolina State University; University of Southern California
摘要：We develop inference procedures for longitudinal data where some of the measurements are censored by fixed constants. We consider a semi-parametric quantile regression model that makes no distributional assumptions. Our research is motivated by the lack of proper inference procedures for data from biomedical studies where measurements are censored due to a fixed quantification limit. In such studies the focus is often on testing hypotheses about treatment equality. To this end, we propose a ra...
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作者：Chen, Jiahua; Li, Pengfei
作者单位：University of British Columbia; University of Alberta
摘要：Normal mixture distributions are arguably the most important mixture models. and also the most technically challenging. The likelihood function of the normal mixture model is unbounded based oil a set of random samples, unless an artificial bound is placed oil its component variance parameter. Moreover, the model is not strongly identifiable so it is hard to differentiate between over dispersion caused by the presence of a mixture and that caused by a large variance, and it has infinite Fisher...
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作者：De Blasi, Pierpaolo; Peccati, Giovanni; Prunster, Igor
作者单位：University of Turin; Universite Paris Nanterre; Universite Paris Saclay
摘要：An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behavior of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic function...
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作者：Lan, Yan; Banerjee, Moulinath; Michailidis, George
作者单位：University of Michigan System; University of Michigan; Abbott Laboratories
摘要：We consider the problem of locating a jump discontinuity (chan-e-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding responses. Budget constraints dictate that a total of n such measurements can be obtained. A multistage adaptive procedure is proposed, where at each stage an estimate of the change point is obtained and new points are sampled from its appropriately chosen neigh...
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作者：Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.
作者单位：University of Rome Tor Vergata; Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called needlets. We establish a minimax result and prove its optimality. We are motivated by astrophysical applications, in particular in connection with the analysis of ultra high-energy cosmic rays.
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作者：Tokdar, Surya T.; Martin, Ryan; Ghosh, Jayanta K.
作者单位：Carnegie Mellon University; Purdue University System; Purdue University; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：Mixture models have received considerable attention recently and Newton [Sankhya Ser A 64 (2002) 306-322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive estimate in the weak topology under mild conditions on the family of densities being mixed. This recursive estimate depends on the data ordering and a permutation-invariant modification is proposed, which is an average of the original over permutations of the data se...
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作者：Zhou, Zhou; Wu, Wei Biao
作者单位：University of Chicago
摘要：We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear quantile estimates under a mild short-range dependence condition. Our results are applied to environmental data sets. In particular, our results can be used to address the problem of whether climate variability has changed, an important problem raised by IPCC (Intergovernmental Panel on Climate Change) in 2001.
