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作者：Goldstein, Larry; Reinert, Gesine
作者单位：University of Southern California; University of Southern California
摘要：Let W be a random variable with mean zero and variance sigma(2). The distribution of a variate W*, satisfying EWf(W). = sigma 2Ef' (W*). for smooth functions f, exists uniquely and defines the zero bias transformation on the distribution of W. The zero bias transformation shares many interesting properties with the well-known size bias transformation for nonnegative variables, but is applied to variables taking on both positive and negative values. The transformation can also be defined on mor...
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作者：Calvin, James M.
作者单位：New Jersey Institute of Technology
摘要：We describe a class of adaptive algorithms for approximating the global minimum of a continuous function on the unit interval. The limiting distribution of the error is derived under the assumption of Wiener measure on the objective functions. For any delta > 0, we construct an algorithm which has error converging to zero at rate n(-(1-delta)) in the number of function evaluations n. This convergence rate contrasts with the n(-1/2) rate of previously studied nonadaptive methods.
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作者：Hall, Peter; Raimondo, Marc
作者单位：Australian National University; Commonwealth Scientific & Industrial Research Organisation (CSIRO)
摘要：Throw a straight line at random into a plane, within which is inscribed a square grid. Color black each grid vertex that lies above the line, and white each vertex below it. Now remove the line, and attempt to reconstruct it from the pattern of vertex colors in an m x m section of the grid. We show that for all epsilon > 0, the line can be approximated to within order m(-1) (log m)(log log m)(1+epsilon), with probability 1, and that there is no deterministic subsequence along which the best ac...
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作者：Stefanov, V. T.; Pakes, A. G.
作者单位：University of Western Australia
摘要：A new and unified approach is presented for constructing joint generating functions for quantities of interest associated with pattern formation in binary sequences. The method is based on results on exponential families of Markov chains. The tools we use are not only new for this area; they seem to be the right approach for deriving general explicit distributional results.
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作者：Yao, Yi-Ching
作者单位：Academia Sinica - Taiwan; Colorado State University System; Colorado State University Fort Collins
摘要：For an infinite sequence of independent and identically distributed (i.i.d.) random variables, the k-record process consists of those terms that are the kth largest at their appearance. Ignatov's theorem states that the k-record processes, k = 1, 2,..., are i.i.d. A new proof is given which is based on a continualization'' argument. An advantage of this fairly simple approach is that Ignatov's theorem can be stated in a more general form by allowing for different tiebreaking rules. In particul...
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作者：Comets, Francis
作者单位：University of California System; University of California Irvine
摘要：We propose a new empirical procedure for detecting phase transition from a single sample of a Gibbs-Markov random field. The method is based on frequencies for large deviations when the whole sample is divided in smaller blocks and estimates for the rate function. We relate our approach to an almost sure large deviation principle.
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作者：Niu, Xu-Feng
作者单位：State University System of Florida; Florida State University; State University System of Florida; Florida State University
摘要：Consider a class of nonstationary time series with the form Y-t = mu t + xi(t) where {xi(t)} is a sequence of infinite moving averages of independent random variables with regularly varying tail probabilities and different scale parameters. In this article, the extreme value theory of {Y-t} is studied. Under mild conditions, convergence results for a point process based on the moving averages are proved, and extremal properties of the nonstationary time series, including the convergence of max...
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作者：Rucinski, A.; Wormald, N. C.
作者单位：Adam Mickiewicz University; University of Melbourne
摘要：Suppose that a process begins with n isolated vertices, to which edges are added randomly one by one so that the maximum degree of the induced graph is always at most 2. In a previous article, the authors showed that as n -> infinity, with probability tending to 1, the result of this process is a graph with n edges. The number of l-cycles in this graph is shown to be asymptotically Poisson (l >= 3), and other aspects of this random graph model are studied.
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作者：Kleptsina, M. L.; Liptser, R. Sh; Serebrovski, A. P.
作者单位：Russian University of Transport; Tel Aviv University
摘要：We give an approximation for optimal filtering estimates of a diffusion type signal and its observation under contamination affecting their drifts. The method of analysis is based on the averaging principle and convergence in total variation for distributions of signal and observation.
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作者：Denardo, Eric V.; Feinberg, Eugene A.; Kella, Offer
作者单位：Yale University; State University of New York (SUNY) System; Stony Brook University; Hebrew University of Jerusalem
摘要：This paper deals with first passage heights of sums of renewal sequences, random walks, and Levy processes. We prove that the joint age and excess (and therefore, the current life. stationary distributions of these heights are stochastically increasing (in the usual first-order sense. in the passage levels. As a preliminary tool, which is also of independent interest, a new decomposition of the stationary excess distribution, as a convolution of two other distributions, is developed. As a cons...
