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作者：PERMAN, M; PITMAN, J; YOR, M
作者单位：Sorbonne Universite; University of California System; University of California Berkeley
摘要：Some general formulae are obtained for size-biased sampling from a Poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function. These formulae explain why in certain cases (gamma and stable) the size-biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking (residual allocation) scheme defined by independent beta random variables. An application is made to length biased sampling of excursion...
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作者：HALL, P; MARRON, JS; PARK, BU
作者单位：Seoul National University (SNU)
摘要：For bandwidth selection of a kernel density estimator, a generalization of the widely studied least squares cross-validation method is considered. The essential idea is to do a particular type of presmoothing of the data. This is seen to be essentially the same as using the smoothed bootstrap estimate of the mean integrated squared error. Analysis reveals that a rather large amount of presmoothing yields excellent asymptotic performance. The rate of convergence to the optimum is known to be be...
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作者：MAMMEN, E; MARRON, JS; FISHER, NI
作者单位：Commonwealth Scientific & Industrial Research Organisation (CSIRO); University of North Carolina; University of North Carolina Chapel Hill
摘要：A test due to B.W. Silverman for modality of a probability density is based on counting modes of a kernel density estimator, and the idea of critical smoothing. An asymptotic formula is given for the expected number of modes. This, together with other methods, establishes the rate of convergence of the critically smoothed bandwidth. These ideas are extended to provide insight concerning the behaviour of the test based on bootstrap critical values.
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作者：VONDRACEK, Z
摘要：Let X(h) be an h-Brownian motion in the unit ball D subset-of R(d) with h harmonic, such that the representing measure of h is not singular with respect to the surface measure on partial derivative D. If Y is a continuous strong Markov process in D with the same killing distributions as X(h), then Y is a time change of X(h). Similar results hold in simply connected domains in C provided with either the Martin or the Euclidean boundary.
