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作者：Bunea, Florentina; Tsybakov, Alexandre B.; Wegkamp, Marten H.
作者单位：State University System of Florida; Florida State University; Sorbonne Universite; Universite Paris Cite
摘要：This paper studies statistical aggregation procedures in the regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of aggregation: model selection (MS) aggregation, convex (C) aggregation and linear (L) aggregation. The objective of (MS) is to select the optimal single estimator from the list; that of (C) is to select the optimal convex combination of the given estimator...
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作者：Mcelroy, Tucker; Politis, Dimitris N.
作者单位：University of California System; University of California San Diego
摘要：A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statistics. The proposed rate estimators are based on simple least squares arguments, and are shown to be accurate in a very general setting without requiring the choice of a tuning parameter. The notion of scanning is introduced with the purpose of extracting useful subsamples of the data series; the proposed rate estimation method is applied to different...
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作者：Finner, Helmut; Dickhaus, Thorsten; Roters, Markus
作者单位：Leibniz Association; Deutsches Diabetes-Zentrum (DDZ); Heinrich Heine University Dusseldorf
摘要：Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing n hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when n tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of p-values. In a general...
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作者：Jiang, Wenxin
作者单位：Northwestern University
摘要：Bayesian variable selection has gained much empirical success recently in a variety of applications when the number K of explanatory variables (x(1),..., x(K)) is possibly much larger than the sample size a. For generalized linear models, if most of the x(j)'s have very small effects on the response y, we show that it is possible to use Bayesian variable selection to reduce overtitting caused by the curse of dimensionality K >> n. In this approach a suitable prior can be used to choose a few o...
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作者：Romano, Joseph P.; Wolf, Michael
作者单位：Stanford University; University of Zurich
摘要：Consider the problem of testing s hypotheses simultaneously. The usual approach restricts attention to procedures that control the probability of even one false rejection, the familywise error rate (FWER). If s is large, one might be willing to tolerate more than one false rejection, thereby increasing the ability of the procedure to correctly reject false null hypotheses. One possibility is to replace control of the FWER by control of the probability of k or more false rejections, which is ca...
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作者：Hall, Peter; Qiu, Pehua
作者单位：University of Melbourne; University of Minnesota System; University of Minnesota Twin Cities
摘要：The removal of blur from a signal, in the presence of noise, is readily accomplished if the blur can be described in precise mathematical terms. However, there is growing interest in problems where the extent of blur is known only approximately, for example in terms of a blur function which depends on unknown parameters that must be computed from data. More challenging still is the case where no parametric assumptions are made about the blur function. There has been a limited amount of work in...
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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：Ben Hariz, Samir; Wylie, Jonathan J.; Zhang, Qiang
作者单位：Le Mans Universite; City University of Hong Kong
摘要：Let (X-i)(i)=1,..., n be a possibly nonstationary sequence such that L(X-i) = P-n, if i <= n theta and L(X-i) = Q(n), if i > n theta, where 0 < theta < 1 is the location of the change-point to be estimated. We construct a class of estimators based on the empirical measures and a seminorm on the space of measures defined through a family of functions F. We prove the consistency of the estimator and give rates of convergence under very general conditions. In particular, the 1/n rate is achieved ...
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作者：Hall, Peter; Meister, Alexander
作者单位：University of Melbourne; University of Stuttgart
摘要：Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely supported and its characteristic function does not ever vanish. Even in these settings, optimal convergence rates are achieved by kernel estimators only when the kernel is chosen to adapt to the unknown smoothness of the target distribution. In this paper we sug...
