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作者：CRITCHLEY, F; MARRIOTT, P; SALMON, M
作者单位：University of Surrey; European University Institute
摘要：A new mathematical object called a preferred point geometry is introduced in order to (a) provide a natural geometric framework in which to do statistical inference and (b) reflect the distinction between homogeneous aspects (e.g., any point theta may be the true parameter) and preferred point ones (e.g., when theta0 is the true parameter). Although preferred point geometry is applicable generally in statistics, we focus here on its relationship to statistical manifolds, in particular to Amari...
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作者：SEIDENFELD, T; WASSERMAN, L
摘要：Suppose that a probability measure P is known to lie in a set of probability measures M. Upper and lower bounds on the probability of any event may then be computed. Sometimes, the bounds on the probability of an event A conditional on an event B may strictly contain the bounds on the unconditional probability of A. Surprisingly, this might happen for every B in a partition B. If so, we say that dilation has occurred. In addition to being an interesting statistical curiosity, this counterintui...
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作者：DAWID, AP; LAURITZEN, SL
作者单位：Aalborg University
摘要：This paper introduces and investigates the notion of a hyper Markov law, which is a probability distribution over the set of probability measures on a multivariate space that (i) is concentrated on the set of Markov probabilities over some decomposable graph, and (ii) satisfies certain conditional independence restrictions related to that graph. A stronger version of this hyper Markov property is also studied. Our analysis starts by reconsidering the properties of Markov probabilities, using a...
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作者：THOMPSON, GL
摘要：Exploratory graphical methods for fully and partially ranked data are proposed. In fully ranked data, n items are ranked in order of preference by a group of judges. In partially ranked data, the judges do not completely specify their ranking of the n items. The resulting set of frequencies is a function on the symmetric group of permutations if the data is fully ranked, and a function on a coset space of the symmetric group if the data is partially ranked. Because neither the symmetric group ...
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作者：BUTLER, RW; DAVIES, PL; JHUN, M
作者单位：University of Duisburg Essen; Korea University
摘要：Consistency is shown for the minimum covariance determinant (MCD) estimators of multivariate location and scale and asymptotic normality is shown for the former. The proofs are made possible by showing a separating ellipsoid property for the MCD subset of observations. An analogous property is shown for the MCD subset computed from the population distribution.
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作者：WU, JS; CHU, CK
作者单位：National Tsing Hua University
摘要：In the fixed-design nonparametric regression model, kernel-type estimators of the locations of jump points and the corresponding sizes of jump values of the regression function are proposed. These kernel-type estimators are analyzed with almost sure results and limiting distributions. Using the limiting distributions, we are able to test the number of jump points and give asymptotic confidence intervals for the sizes of jump values of the regression function. Simulation studies demonstrate tha...
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作者：QIN, J
摘要：It is well known that we can use the likelihood ratio statistic to test hypotheses and to construct confidence intervals in full parametric models. Recently, Owen introduced the empirical likelihood method in nonparametric models. In this paper, we generalize his results to biased sample problems. A Wilks theorem leading to a likelihood ratio confidence interval for the mean is given. Some extensions, discussion and simulations are presented.
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作者：KIM, JH
摘要：We consider general chi-square goodness-of-fit test statistics for randomly censored data-call these generalized Pearson statistics-which are nonnegative definite quadratic forms in the cell frequencies obtained from the product-limit estimator, allowing random cells and general estimators of nuisance parameters. This class of statistics generalizes the class studied by Moore and Spruill in the no censoring case. The large sample behavior of these statistics under the null hypothesis and local...
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作者：LESLIE, J; VANEEDEN, C
作者单位：University of London; Birkbeck University London; University of British Columbia; University of Quebec; University of Quebec Montreal
摘要：Dufour gives a conjecture concerning a characterization of the exponential distribution based on type 2 right censored samples. This conjecture, if true, generalizes the characterization based on complete samples of Seshadri, Csorgo and Stephens (1969) and Dufour, Maag and van Eeden (1984). In this paper it is shown that Dufour's conjecture is true if the number of censored observations is no larger than (1/3)n - 1, where n is the sample size. The result has implications for testing fit of cen...
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作者：LE, HL; KENDALL, DG
作者单位：University of Cambridge
摘要：The Riemannian metric structure of the shape space SIGMA(m)k for k labelled points in R(m) was given by Kendall for the atypically simple situations in which m = 1 or 2 and k greater-than-or-equal-to 2. Here we deal with the general case (m greater-than-or-equal-to 1, k greater-than-or-equal-to 2) by using the properties of Riemannian submersions and warped products as studied by O'Neill. The approach is via the associated size-and-shape space that is the warped product of the shape space and ...
