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闭合指数族中利用复合似然进行最大似然估计AI 解读

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AI 解读

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…

图像形变的惩罚似然方法AI 解读

Summary A warping is a function that deforms images by mapping between image domains. The choice of function is formulated statistically as maximum penalized likelihood, where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping. The paper addresses two issues simultaneously, of how to choose the warping function and how to assess the alignment. A new, Fourier–von Mises image model is identified, with…

标志点数据的大小与形状分析AI 解读

The paper deals with statistical analysis of landmark data using the exact joint distribution theory for the size and shape of planar Gaussian configurations. This is an extension of earlier work which considered marginal shape analysis. Special cases of the size and shape distribution are examined and the isotropic Gaussian model is investigated in particular detail. Various properties are studied, including conditional distributions and a curve of regression. Finally we…

标志点数据的大小与形状分析AI 解读

The paper deals with statistical analysis of landmark data using the exact joint distribution theory for the size and shape of planar Gaussian configurations. This is an extension of earlier work which considered marginal shape analysis. Special cases of the size and shape distribution are examined and the isotropic Gaussian model is investigated in particular detail. Various properties are studied, including conditional distributions and a curve of regression. Finally we…

拟合优度与独立性的 Rao 得分检验AI 解读

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.

形状数据的统计分析AI 解读

The paper deals with the statistical shape analysis of landmark data. Bookstein (1986) introduced a plausible model and obtained a useful normal approximation for three landmarks. We use exact distribution theory and a normal approximation to consider maximum likelihood estimation. The Fisher information matrix for the normal approximation is given and we consider the hypothesis of shape change. Using these results, we analyse a practical example based on digitized shapes.…

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空间线性模型中似然的多峰性AI 解读

A popular covariance scheme used for the spatial linear model in geostatistics has spherical form. However, the likelihood is not twice differentiable with respect to the range parameter, and this raises some questions regarding the unimodality of the likelihood. We compare the likelihoods of the spatial linear model for small samples under this scheme and the doubly geometric scheme. Also, a power covariance with range parameter is proposed. In view of potential multimodal…

形状数据的统计分析AI 解读

The paper deals with the statistical shape analysis of landmark data. Bookstein (1986) introduced a plausible model and obtained a useful normal approximation for three landmarks. We use exact distribution theory and a normal approximation to consider maximum likelihood estimation. The Fisher information matrix for the normal approximation is given and we consider the hypothesis of shape change. Using these results, we analyse a practical example based on digitized shapes.…

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von Mises–Fisher 分布的拟合优度检验AI 解读

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.

空间回归中残差协方差模型的最大似然估计AI 解读

We describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters. Observations are assumed to be Gaussian. We give conditions which ensure consistency and asymptotic normality of the estimators. Our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small…

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方向数据的一般相关系数及相关回归问题AI 解读

A correlation coefficient ρ2 is proposed for bivariate angular distributions and for bivariate distributions on general manifolds. In the cylindrical case ρ2 is the coefficient of Mardia (1976), and for the bivariate angular case it is a modified version of the correlation coefficient of Mardia & Puri (1978). Some properties of ρ2 are examined and compared with those of other bidirectional correlation coefficients. In particular, this coefficient is found to be closely…

矩阵 von Mises–Fisher 与 Bingham 分布的极大似然估计AI 解读

It has been conjectured by Khatri and Mardia that with probability one MLEs for the parameters of the von Mises-Fisher matrix distribution exist and are unique. We prove that, except for small sample sizes, this conjecture is true, both in the case where the parameter matrix has known rank and in the unrestricted case. The corresponding result for the matrix Bingham distribution is proven also.

对尺度稳健的球面相关系数AI 解读

There are several bidirectional situations where it is required to obtain a measure of correlation. The question has been raised often that the bidirectional correlation coefficients so far known are not scale invariant, even asymptotically in the sense that their asymptotic distributions under the hypothesis of independence with von Mises marginals depend upon concentration parameters. Following a conditional approach of Cox (1975), we introduce a new correlation…

球面上的小圆分布AI 解读

A new distribution is proposed as a model for measurements of direction that cluster near a small circle, i.e. parallel of latitude, on the sphere. It is a generalization of both the Fisher-von Mises and Dimroth-Watson distributions. Methods of estimation and inference are discussed and an approximation that is valid for large values of the shape parameter is introduced. The use of the distribution is illustrated by the analysis of artificially generated data

球面上的小圆分布AI 解读

A new distribution is proposed as a model for measurements of direction that cluster near a small circle, i.e. parallel of latitude, on the sphere. It is a generalization of both the Fisher-von Mises and Dimroth-Watson distributions. Methods of estimation and inference are discussed and an approximation that is valid for large values of the shape parameter is introduced. The use of the distribution is illustrated by the analysis of artificially generated data

圆柱面变量模型及其应用AI 解读

Summary A suitable model when two random variables take values on a cylinder is proposed and its main properties are discussed. The maximum likelihood estimators for the parameters of the model are obtained and a likelihood ratio test of independence is derived. A numerical example is given.

方向统计中的 von Mises–Fisher 矩阵分布AI 解读

Summary When n distinguishable directions in p dimensions are required to describe each orientation, Downs (1972) has extended the von Mises–Fisher distribution. We obtain the normalizing constant which leads to the investigation of various basic properties of the distribution. In particular, an explicit expression for the first population moment as well as the asymptotic distribution of the basic statistics are provided. The estimation problem, important testing problems,…

von Mises–Fisher 分布的贝叶斯推断AI 解读

The main aim of this note is to give a theoretical discussion of Bayesian inference for the von Mises-Fisher distribution. The choice of particular priors is considered and the admissibility of certain Bayesian estimators studied. For the multisample case estimators are given. Some problems of testing hypotheses are summarized in the form of posterior odds against the null hypothesis.