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作者：Bentkus, V; Götze, F; van Zwet, WR
作者单位：University of Bielefeld; Leiden University; Leiden University - Excl LUMC; University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the validity of an Edgeworth expansion with remainder O(N-1) under Cramer's condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder o(N-1) without imposing additional assumptions on the structure of ...
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作者：Haussler, D; Opper, M
作者单位：University of California System; University of California Santa Cruz; University of Wurzburg
摘要：Assume (P-theta: theta epsilon Theta) is a set of probability distributions with a common dominating measure on a complete separable metric space Y. A state theta* epsilon Theta is chosen by Nature. A statistician obtains n independent observations Y-1,...,Y-n from Y distributed according to P-theta.. For each time t between 1 and n, based on the observations Y-1,...,Yt-1, the statistician produces an estimated distribution (P) over cap(t) for P-theta* and suffers a loss L(P-theta., (P) over c...
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作者：Birgé, L
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：The Grenander estimator of a decreasing density, which is defined as the derivative of the concave envelope of the empirical c.d.f, is known to be a very good estimator of an unknown decreasing density on the half-line R+ when this density is not assumed to be smooth. It is indeed the maximum likelihood estimator and one can get precise upper bounds for its risk when the loss is measured by the L-1-distance between densities. Moreover, if one restricts oneself to the compact subsets of decreas...
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作者：Mammen, E; Van de Geer, S
作者单位：Ruprecht Karls University Heidelberg; Leiden University - Excl LUMC; Leiden University
摘要：Consider a partial linear model, where the expectation of a random variable Y depends on covariates (x, z) through F(theta(o)x + m(o)(z)), with theta(o) an unknown parameter, and m(o) an unknown function. We apply the theory of empirical processes to derive the asymptotic properties of the penalized quasi-likelihood estimator.
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作者：Tsybakov, AB
作者单位：Sorbonne Universite; Russian Academy of Sciences
摘要：Let X-1,...,X-n be independent identically distributed observations from an unknown probability density f((.)). Consider the problem of estimating the level set G = G(f)(lambda)= (x epsilon R-2: f(x) greater than or equal to lambda) from the sample X-1,...,X-n, under the assumption that the boundary of G has a certain smoothness. We propose piecewise-polynomial estimators of G based on the maximization of local empirical excess masses. We show that the estimators have optimal rates of converge...
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作者：Cuesta-Albertos, JA; Gordaliza, A; Matrán, C
作者单位：Universidad de Cantabria; Universidad de Valladolid
摘要：A class of procedures based on impartial trimming (self-determined by the data) is introduced with the aim of robustifying k-means, hence the associated clustering analysis. We include a detailed study of optimal regions, showing that only nonpathological regions can arise from impartial trimming procedures. The asymptotic results provided in the paper focus on strong consistency of the suggested methods under widely general conditions. A section is devoted to exploring the performance of the ...
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作者：Drost, FC; Klaassen, CAJ; Werker, BJM
作者单位：Tilburg University; Tilburg University; University of Amsterdam
摘要：In a framework particularly suited for many time-series models we obtain a LAN result under quite natural and economical conditions. This enables us to construct adaptive estimators for (part of) the Euclidean parameter in these semiparametric models. Special attention is directed to group models in time series with the important subclass of models with time varying location and scale. Our set-up is confronted with the existing literature and, as examples, we reconsider linear regression and A...
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作者：Steif, JE
作者单位：Chalmers University of Technology
摘要：The joint distribution of a d-dimensional random field restricted to a box of size k can be estimated by looking at a realization in a box of size n >> k and computing the empirical distribution. This is done by sliding a box of size a around in the box of size n and computing frequencies. We show that when k = ii(n) grows as a function of n, then the total variation distance between this empirical distribution and the true distribution goes to 0 a.s. as n --> infinity provided k(n)(d) less th...
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作者：Bedford, T; Meilijson, I
作者单位：Delft University of Technology; Tel Aviv University
摘要：It is well known that the joint distribution of a pair of lifetime variables X-1 and X-2 which right censor each other cannot be specified in terms of the subsurvival functions P(X-2 > X-1 > x), P(X-1 > X-2 > x) and P(X-1 = X-2 > x) without additional assumptions such as independence of X-1 and X-2. For many practical applications independence is an unacceptable assumption, for example, when X-1 is the lifetime of a component subjected to maintenance and X-2 is the inspection time. Peterson pr...
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作者：Dorado, C; Hollander, M; Sethuraman, J
作者单位：State University System of Florida; Florida State University
摘要：The construction and analysis of repair models is an important area in reliability. A commonly used model is the minimal repair model. Under this model, repair restores the state of the system to its level prior to failure. Kijima introduced repair models that could be classified as better-than-minimal. Under Kijima's models, the system, upon repair, is functionally the same as a working system of lesser age which has never experienced failure. In this paper, we present a new approach to the m...
