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作者：Bühlmann, P
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We propose a sieve bootstrap procedure for time series with a deterministic trend. The sieve for constructing the bootstrap is based on nonparametric trend estimation and autoregressive approximation for some noise process. The bootstrap scheme itself does i.i.d, resampling of estimated innovations from fitted autoregressive models. We show the validity and indicate second-order correctness of such sieve bootstrap approximations for the limiting distribution of nonparametric linear smoothers. ...
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作者：Tsybakov, AB
作者单位：Sorbonne Universite
摘要：The problem of nonparametric function estimation in the Gaussian white noise model is considered. It is assumed that the unknown function belongs to one of the Sobolev classes, with an unknown regularity parameter. Asymptotically exact adaptive estimators of functions are proposed on the scale of Sobolev classes, with respect to pointwise and sup-norm risks. It is shown that, unlike the case of L-2-risk, a loss of efficiency under adaptation is inevitable here. Bounds on the value of the loss ...
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作者：Stute, W; Thies, S; Zhu, LX
作者单位：Justus Liebig University Giessen; Chinese Academy of Sciences
摘要：In the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus, smooth and directional goodness-of-fit tests. Since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain, we propose to replace this process by its innovation martingale. It turns out that the resulting tests are (asymptotically) distribution free under composite null models and may ...
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作者：Studeny, M; Bouckaert, RR
作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; Prague University of Economics & Business; Utrecht University
摘要：A chain graph (CG) is a graph admitting both directed and undirected edges with (partially) directed cycles forbidden. It generalizes both the concept of undirected graph (UG) and the concept of directed acyclic graph (DAG). A chain graph can be used to describe efficiently the conditional independence structure of a multidimensional discrete probability distribution in the form of a graphoid, that is, in the form of a list of statements X is independent of Y given Z obeying a set of five prop...
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作者：Hall, P; Raimondo, M
作者单位：Australian National University
摘要：Approximating boundaries using data recorded on a regular grid induces discrete rounding errors in both vertical and horizontal directions. In cases where grid points exhibit at least some degree of randomness, an extensive theory has been developed for local-polynomial boundary estimators. It is inapplicable to regular grids, however. In this paper we impose strict regularity of the grid and describe the performance of local linear estimators in this context. Unlike the case of classical curv...
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作者：Putter, H; van Zwet, WR
作者单位：University of Amsterdam; Academic Medical Center Amsterdam; Leiden University - Excl LUMC; Leiden University
摘要：In this paper the validity of a one-term Edgeworth expansion for Studentized symmetric statistics is proved. We propose jackknife estimates for the unknown constants appearing in the expansion and prove their consistency. As a result we obtain the second-order correctness of the empirical Edgeworth expansion for a very general class of statistics, including U-statistics, L-statistics and smooth functions of the sample mean. We illustrate the application of the bootstrap in the case of a U-stat...
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作者：Wang, JL; Müller, HG; Capra, WB
作者单位：University of California System; University of California Davis
摘要：This paper provides a data analysis and some methodological advances which contribute to an ongoing scientific debate about the patterns of aging. One of the problems we address is how to estimate a hazard function when only aggregated information on the lifetimes in the form of a lifetable is available. This problem affects the estimation of oldest-old mortality which in turn plays an important role in the quantification of biological lifespan and longevity. We illustrate these issues with an...
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作者：Adrover, JG
作者单位：National University of Cordoba
摘要：Maronna defines affine equivariant M-estimators for multivariate location and scatter. They are particularly suited for estimating the pseudo-covariance or scatter matrix of an elliptical population. By defining the bias of a dispersion matrix properly, we consider the maximum bias of an M-estimator over an E-neighborhood of the underlying elliptical distribution (location known). We find that Tyler's estimator minimizes the maximum bias.
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作者：Singh, K
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：A general formula for computing the breakdown point (in robustness) for the tth bootstrap quantile of a statistic T-n is obtained. The answer depends on t and the breakdown point of T-n. Since the bootstrap quantiles are vital ingredients of bootstrap confidence intervals, the theory has implications pertaining to robustness of bootstrap confidence intervals. For certain L and M estimators, a robustification of bootstrap is suggested via the notion of Winsorization.
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作者：Davies, PL
作者单位：University of Duisburg Essen
摘要：This article gives two constructions of a weighted mean which has a large domain, is affinely equivariant, has a locally high breakdown point and is locally uniformly linearizable. One construction is based on M-functionals with smooth defining psi- and chi-functions which are used to control the weighting. The second construction involves a locally uniformly linearizable reduction of the data to a finite set of points. This construction has the advantage of computational speed and opens up th...
