-
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...
-
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...
-
作者：Mao, Chang Xuan; Lindsay, Bruce G.
作者单位：University of California System; University of California Riverside; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one-sided. Confidence intervals for the number of classes are also necessarily one-sided. A sequence of lower bounds to the odds is developed and use...
-
作者：Morgan, J. P.; Reck, Brian H.
作者单位：Virginia Polytechnic Institute & State University; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information matrix and consequently given in terms of block concurrences. Equalizing block concurrences for given block sizes is often, but not always, the best strategy. Sufficient conditions are established for various strong optimalities and a detailed study of E-op...
-
作者：Stufken, John; Tang, Boxin
作者单位：University System of Georgia; University of Georgia; Simon Fraser University
摘要：Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d + 2 constraints for any d and any run size n = lambda 2(d). Our results not only give the number of nonisomorphic orthogonal arrays for given d...
-
作者：Jager, Leah; Wellner, Jon A.
作者单位：Grinnell College; University of Washington; University of Washington Seattle
摘要：A unified family of goodness-of-fit tests based on phi-divergences is introduced and studied. The new family of test statistics S-n(s) includes both the supremum version of the Anderson-Darling statistic and the test statistic of Berk and Jones [Z. Wahrsch. Verw. Gebiete 47 (1979) 47-59] as special cases (s = 2 and s = 1, resp.). We also introduce integral versions of the new statistics. We show that the asymptotic null distribution theory of Berk and Jones [Z. Wahrsch. Verw. Gebiete 47 (1979)...
-
作者：Letac, Gerard; Massam, Helene
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; York University - Canada
摘要：When considering a graphical Gaussian model N-G Markov with respect to a decomposable graph G, the parameter space of interest for the precision parameter is the cone PG of positive definite matrices with fixed zeros corresponding to the missing edges of G. The parameter space for the scale parameter of N-G is the cone Q(G), dual to P-G, of incomplete matrices with submatrices corresponding to the cliques of G being positive definite. In this paper we construct on the cones Q(G) and P-G two fa...
-
作者：Audibert, Jean-Yves; Tsybakov, Alexandre B.
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Sorbonne Universite
摘要：It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than n(-1/2). The work on this subject has suggested the following two conjectures: (i) the best achievable fast rate is of the order n(-1), and (ii) the plug-in classifiers generally converge more slowly than the classifiers based on empirical risk minimization. We show that both conjectures are not correct. In...
-
作者：Gloter, Arnaud; Hoffmann, Marc
作者单位：Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We estimate the Hurst parameter H of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of H more difficult since relevant information is mostly contained in the high frequencies of the signal. We quantify the difficulty of the statistical problem in a min-max sense: we prove that the rate n(-1/(4H+2)) is optimal for estimating H and propose rate optimal estimators based on adaptive...
-
作者：Lahiri, P.; Mukherjee, Kanchan
作者单位：University System of Maryland; University of Maryland College Park; University of Liverpool
摘要：We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to finite population sampling. We also suggest three different measures of uncertainty of our proposed e...
