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作者：Albers, W; Boon, PC; Kallenberg, WCM
作者单位：University of Twente
摘要：A pretest procedure consists of a preliminary test on a nuisance parameter, investigating whether it equals a given value or not, followed by the main testing problem on the parameter of interest. In case of acceptance of the preliminary test, the main test is applied in the restricted family with the given value of the nuisance parameter, while otherwise the test is performed in the complete family, including the nuisance parameter. For an appropriate class of tests, containing all standard f...
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作者：Hall, P; Heckman, NE
作者单位：Australian National University; University of British Columbia
摘要：A new approach to testing. for monotonicity of a regression mean, not requiring computation of a curve estimator or a bandwidth, is suggested. It is based on the notion of running gradients over short, intervals, although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip/excess mass approach for testing modality hypotheses about densities. Like the latter methods, the new technique does not suffer difficulties caused by almost-Bat parts of the target fu...
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作者：Picard, D; Tribouley, K
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around f(x(0)), in either a white noise model or a regression setting. A suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor. The procedure does not require knowledge of the regularity of the unknown function f; it is also efficient for functions with a low degree of regul...
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作者：Politis, K; Pitts, SM
作者单位：University of Southampton; University of Cambridge
摘要：Nonparametric estimators of solutions of renewal-type equations are proposed in terms of the empirical renewal function. Using the approach of Grubel and Pitts [Ann. Stat. 21 1431-1451(1993)], who studied asymptotic properties of the empirical renewal function, a number of properties of our estimators are established, including strong consistency, asymptotic normality and efficiency, and asymptotic validity of bootstrap confidence bounds. The results are illustrated by some particular examples.
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作者：Inglot, T; Kallenberg, WCM; Ledwina, T
作者单位：Wroclaw University of Science & Technology; University of Twente; Polish Academy of Sciences
摘要：The shortcoming of a test is the difference between the maximal attainable power and the power of the test under consideration. Vanishing shortcoming, when the number of observations tends to infinity, is therefore an optimality property of a test. Other familiar optimality criteria are based on the asymptotic relative efficiency of the test. The relations between these optimality criteria are investigated. It turns out that vanishing shortcoming is seemingly slightly stronger than first-order...
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作者：Owen, AB
作者单位：Stanford University
摘要：Some standard numerical problems become intractable in high dimensions. Yet successes are often achieved in practice. This may be explained in terms of the underlying target function being somehow simpler than assumed in the intractability arguments. A prototypical form of simplicity is approximate linearity. In moderate dimensions, linearity can be investigated by linear regression. In very high dimensions, this becomes computationally inefficient and eventually infeasible, as the cost of reg...
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作者：Almudevar, A; Field, C; Robinson, J
作者单位：Saint Marys University - Canada; Dalhousie University; University of Sydney
摘要：When a unique M-estimate exists, its density is obtained as a corollary to a more general theorem which asserts that under mild conditions the intensity function of the point process of solutions of the estimating equations exists and is given by the density of the estimating function standardized by multiplying it by the inverse of its derivative. We apply the results to give a result for Huber's proposal 2 applied to regression and scale estimates. We also give a saddlepoint approximation fo...
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作者：Janssen, A
作者单位：Heinrich Heine University Dusseldorf
摘要：It is shown that the global power function of any nonparametric test is flat on balls of alternatives except for alternatives coming from a finite dimensional subspace. The present benchmark is here the upper one-sided (or two-sided) envelope power function. Every choice of a test fixes a priori a finite dimensional region with high power. It turns out that also the level points are far away from the corresponding Neyman-Pearson test level points except for a finite number of orthogonal direct...
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作者：Dress, H; de Haan, L; Resnick, S
作者单位：University of Cologne; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam; Cornell University
摘要：An abundance of high quality data sets requiring heavy tailed models necessitates reliable methods of estimating the shape parameter governing the degree of tail heaviness. The Will estimator is a popular method for doing this but its practical use is encumbered by several difficulties. We show that an alternative method of plotting Hill estimator values is more revealing than the standard method unless the underlying data comes from a Pareto distribution.
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作者：Yang, Y
作者单位：Iowa State University
摘要：General results on adaptive density estimation are obtained with respect to any countable collection of estimation strategies under Rullback-Leibler and squared L-2 losses. It is shown that without knowing which strategy works best for the underlying density, a single strategy can be constructed by mixing the proposed ones to be adaptive in terms of statistical risks. A consequence is that under some mild conditions, an asymptotically minimax-rate adaptive estimator exists for a given countabl...
