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Gneiting 时空协方差模型中的凹陷现象
Gneiting (2002) proposed a nonseparable covariance model for spatial-temporal data. In present paper we show that in certain circumstances his model possesses a counterintuitive “dimple”, which detracts from its modelling appeal.
闭合指数族中利用复合似然进行最大似然估计
In certain multivariate problems the full probability density has an awkward normalizing constant, but the conditional and/or marginal distributions may be much more tractable. In this paper we investigate the use of composite likelihoods instead of the full likelihood. For closed exponential families, both are shown to be maximized by the same parameter values for any number of observations. Examples include log-linear models and multivariate normal models. In other cases…
复 Bingham 四次分布与形状分析
Summary The complex Bingham distribution was introduced by Kent as a tractable model for landmark-based shape analysis. It forms an exponential family with a sufficient statistic which is quadratic in the data. However, the distribution has too much symmetry to be widely useful. In particular, under high concentration it behaves asymptotically as a normal distribution, but where the covariance matrix is constrained to have complex symmetry. To overcome this limitation and to…
拟合优度与独立性的 Rao 得分检验
Rao's score statistic is a standard tool for carrying out hypothesis tests. A unified approach is given which encompasses many common tests. When a suitable group structure is present, it is shown how the derivation of the test statistic can be simplified. An omnibus test of multivariate normality is derived as an example of group invariance. As another application of Rao score tests, a general method is given for constructing tests of independence.
von Mises–Fisher 分布的拟合优度检验
SUMMARY We derive a goodness-of-fit test for the von Mises-Fisher distribution which is an extension of a goodness-of-fit test for the von Mises distribution given by Cox (1975). A robust version of the test is also given. Computational aspects of the test statistic are discussed and a numerical example is given.