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作者：Mukerjee, R; Wu, CFJ
作者单位：University of Michigan System; University of Michigan
摘要：We develop a combinatorial condition necessary for the existence of a saturated asymmetrical orthogonal array of strength 2. This condition Limits the choice of integral solutions to the system of equations in the Bose-Bush approach and can thus strengthen considerably the Bose-Bush approach as applied to a symmetrical part of such an array. As a consequence, several nonexistence results follow for saturated and nearly saturated orthogonal arrays of strength 2. One of these leads to a partial ...
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作者：EFROMOVICH, S
摘要：The problem is to estimate sequentially a nonparametric function known to belong to an alpha-th-order Sobolev subspace (alpha > 1/2) with a minimax mean stopping time subject to an assigned maximum mean integrated squared error. For the case of a given alpha there exists a sharp estimator which has a minimal constant and a rate of minimax mean stopping time increasing as the assigned risk decreases. The situation changes drastically if alpha is unknown: a necessary and sufficient condition for...
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作者：CSORGO, S; MIELNICZUK, J
作者单位：Polish Academy of Sciences; Institute of Computer Science of the Polish Academy of Sciences
摘要：Dehling and Taqqu established the weak convergence of the empirical process for a long-range dependent stationary sequence under Gaussian subordination. We show that the corresponding density process, based on kernel estimators of the marginal density, converges weakly with the same normalization to the derivative of their limiting process. The phenomenon, which carries on for higher derivatives and for functional laws of the iterated logarithm, is in contrast with independent or weakly depend...
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作者：HALL, P; HU, TC; MARRON, JS
作者单位：National Tsing Hua University; University of North Carolina; University of North Carolina Chapel Hill
摘要：Variable window width kernel density estimators, with the width varying proportionally to the square root of the density, have been thought to have superior asymptotic properties. The rate of convergence has been claimed to be as good as those typical for higher-order kernels, which makes the variable width estimators more attractive because no adjustment is needed to handle the negativity usually entailed by the latter. However, in a recent paper, Terrell and Scott show that these results can...
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作者：Xu, Y; Martinsek, AT
摘要：This paper proposes a fully sequential procedure for constructing a fixed-width confidence band for an unknown density on a finite interval and shows the procedure has the desired coverage probability asymptotically as the width of the band approaches zero. The procedure is based on a result-of Bickel and Rosenblatt. Its implementation in the sequential setting cannot be obtained using Anscombe's theorem, because the normalized maximal deviations between the kernel estimate and the true densit...
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作者：Andrews, DWK; Ploberger, W
作者单位：Technische Universitat Wien
摘要：This paper establishes the asymptotic admissibility of the likelihood ratio (LR) test for a general class of testing problems in which a nuisance parameter is present only under the alternative hypothesis. The paper also establishes the finite sample admissibility of the LR test for testing problems of this sort that arise in Gaussian linear regression models with known variance.
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作者：HENGARTNER, NW; STARK, PB
作者单位：Yale University
摘要：A conservative finite-sample simultaneous confidence envelope for a density can be found by solving a finite set of finite-dimensional linear programming problems if the density is known to be monotonic or to have at most it modes relative to a positive weight function. The dimension of the problems is at most (n/log n)(1/3), where n is the number of observations. The linear programs find densities attaining the largest and smallest values at a point among cumulative distribution functions in ...
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作者：Grund, B; Hall, P
作者单位：Australian National University
摘要：We show that, for L(p) convergence of the mode of a nonparametric density estimator to the mode of an unknown probability density, finiteness of the pth moment of the underlying distribution is both necessary and sufficient. The basic requirement of existence of finite variance has been overlooked by statisticians, who have earlier considered mean square convergence of nonparametric mode estimators; they have focussed on mean squared error of the asymptotic distribution, rather than an asympto...
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作者：Gustafson, P; Wasserman, L
作者单位：Carnegie Mellon University
摘要：We investigate diagnostics for quantifying the effect of small changes to the prior distribution over a h-dimensional parameter space. We show that several. previously suggested diagnostics, such as the norm of the Frechet derivative, diverge at rate n(k/2) if the base prior is an interior point in the class of priors, under the density ratio topology. Diagnostics based on phi-divergences exhibit similar asymptotic behavior. We show that better asymptotic behavior can be obtained by suitably r...
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作者：Hall, P; Lahiri, SN; Polzehl, J
作者单位：Zuse Institute Berlin; Iowa State University
摘要：We analyse methods based on the block bootstrap and leave-out cross-validation, for choosing the bandwidth in nonparametric regression when errors have an almost arbitrarily long range of dependence. A novel analytical device for modelling the dependence structure of errors is introduced. This allows a concise theoretical description of the way in which the range of dependence affects optimal bandwidth choice. It is shown that, provided block length or leave-out number, respectively, are chose...
