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作者：Lopuhaä, HP
作者单位：Delft University of Technology
摘要：We investigate the asymptotic behavior of a weighted sample mean and covariance, where the weights are determined by the Mahalanobis distances with respect to initial robust estimators. We derive an explicit expansion for the weighted estimators. From this expansion it can be seen that reweighting does not improve the rate of convergence of the initial estimators. We also show that if one uses smooth S-estimators to determine the weights, the weighted estimators are asymptotically normal. Fina...
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作者：Eggermont, PPB; LaRiccia, VN
作者单位：University of Delaware
摘要：We study maximum penalized likelihood density estimation using the first roughness penalty functional of Good. We prove a simple pointwise comparison result with a kernel estimator based on the two-sided exponential kernel. This leads to L(1) convergence results similar to those for kernel estimators. We also prove Hellinger distance bounds for the roughness penalized estimator.
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作者：Van Keilegom, I; Akritas, MG
作者单位：Maastricht University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：Consider a heteroscedastic regression model Y = m(X) + sigma(X)epsilon, where the functions m and sigma are smooth, and epsilon is independent of X. The response variable Y is subject to random censoring, but it is assumed that there exists a region of the covariate X where the censoring of Y is light. Under this condition, it is shown that the assumed nonparametric regression model can be used to transfer tail information from regions of light censoring to regions of heavy censoring. Crucial ...
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作者：Babu, GJ; Pathak, PK; Rao, CR
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Michigan State University
摘要：Rao, Pathak and Koltchinskii have recently studied a sequential approach to resampling in which resampling is carried out sequentially one-by-one (with replacement each time) until the bootstrap sample contains m approximate to (1 - e(-1))n approximate to 0.632n distinct observations from the original sample. In our previous work, we have established that the main empirical characteristics of the sequential bootstrap go through, in the sense of being within a distance O(n(-3/4)) from those of ...
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作者：Lin, CY; Kosorok, MR
作者单位：University of Alabama System; University of Alabama Birmingham; University of Wisconsin System; University of Wisconsin Madison
摘要：Many of the popular nonparametric test: statistics for censored survival data used in two-sample, K-sample trend and continuous covariate situations are special cases of a general statistic, differing only in the choice of the covariate-based label and the weight function. A weight function determines the asymptotic efficiency of its corresponding statistic in this general class. Since the true alternatives are often unknown, we may not be able to foresee which weight function is the best for ...
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作者：Mammen, E; Linton, O; Nielsen, J
作者单位：Ruprecht Karls University Heidelberg; Yale University
摘要：We derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function. The procedure employs a recent projection interpretation of popular kernel estimators provided by Mammen, Marron, Turlach and Wand and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in Bickel, Klaassen, Ritov and Wellner. Our procedure achieves the same bias and variance as the oracle...
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作者：Fan, JQ; Zhang, WY
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Chinese University of Hong Kong
摘要：Varying coefficient models are a useful extension of classical linear models. They arise naturally when one wishes to examine how regression coefficients change over different groups characterized by certain covariates such as age. The appeal of these models is that the coefficient functions can easily be estimated via a simple local regression. This yields a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when different coefficient functions admit d...
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作者：Yang, YH; Barron, A
作者单位：Iowa State University; Yale University
摘要：We present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rales of convergence.
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作者：Gassiat, E; Gautherat, E
作者单位：Universite Paris Saclay; Universite de Reims Champagne-Ardenne
摘要：In a recent paper, we proposed a new estimation method for the blind deconvolution of a linear system with discrete random input, when the observations may be noise perturbed. We give here asymptotic properties of the estimators in the parametric situation. With nonnoisy observations, the speed of convergence is governed by the Ii-tail of the inverse filter. which may have an exponential decrease. With noisy observations, the estimator satisfies a limit theorem with known distribution, which a...
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作者：Bai, ZD; He, XM
作者单位：National University of Singapore; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We derive the asymptotic distribution of the maximal depth regression estimator recently proposed in Rousseeuw and Hubert. The estimator is obtained by maximizing a projection-based depth and the limiting distribution is characterized through a max-min operation of a continuous process. The same techniques can be used to obtain the limiting distribution of some other depth estimators including Tukey's deepest point based on half-space depth. Results for the special case of two-dimensional prob...
