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基于含噪支持函数数据的凸集估计AI 解读

In problems of medical imaging and robotic vision, measurements of a convex set are sometimes obtained via the set's support function. The standard way in which the convex set is recovered from such data is to suppose that it is polygonal, model the errors as Normal random variables, and apply constrained maximum likelihood methods. Typically, the number of sides assumed of the polygon is equal to or a little less than the number of data points. However, from a statistical…

由含噪支持函数数据估计凸集AI 解读

In problems of medical imaging and robotic vision, measurements of a convex set are sometimes obtained via the set's support function. The standard way in which the convex set is recovered from such data is to suppose that it is polygonal, model the errors as Normal random variables, and apply constrained maximum likelihood methods. Typically, the number of sides assumed of the polygon is equal to or a little less than the number of data points. However, from a statistical…

球面数据的核密度估计AI 解读

We study two natural classes of kernel density estimators for use with spherical data. Members of both classes have already been used in practice. The classes have an element in common, but for the most part they are disjoint. However, all members of the first class are asymptotically equivalent to one another, and to a single element of the second class. In this sense the second class ‘contains’ the first. It includes some estimators which out-perform all those in the first…

球面数据的核密度估计AI 解读

We study two natural classes of kernel density estimators for use with spherical data. Members of both classes have already been used in practice. The classes have an element in common, but for the most part they are disjoint. However, all members of the first class are asymptotically equivalent to one another, and to a single element of the second class. In this sense the second class ‘contains’ the first. It includes some estimators which out-perform all those in the first…

预测与最小二乘的效率AI 解读

The general linear model y = Xβ + u is considered when the ranks of X and Γ, the error covariance matrix, are arbitrary. The least squares and best linear unbiased estimators of the part of β in the row space of X are shown to be unique. Necessary and sufficient conditions are given for these estimators to be identical. The treatment deliberately avoids the use of generalized inverses and estimable linear functions. The best linear predictor of y0 = x0’β+ u0 from the general…

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最小二乘回归中的序列相关检验（三）AI 解读

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta…

最小二乘回归中的序列相关检验：第三篇AI 解读

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta…

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圆周上的拟合优度检验（二）AI 解读

A statistical analysis is made by use of the null hypothesis test for random samples which have been drawn from a population with the continuous distribution function F(x). It is useful for distributions on a circle since its value does not depend on the arbitrary point chosen to begin cumulating the probability density and the sample points. Sampling experiments on bird flight are plotted by use of an IBM 650 computer.

回归检验对非正态性的稳健性AI 解读

A number of statistical procedures involve the comparison of a ‘regression’ mean square with a ‘residual’ mean square using the normal-theory F distribution for reference. The use of the procedure for the analysis of actual data implies that the distribution of the mean-square ratio is insensitive to moderate non-normality. Many investigators, in particular Pearson (1931), Geary (1947), Gayen (1950), have considered the sensitivity of this distribution to parent…

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连续分布的卡方拟合优度检验AI 解读

SUMMARY Suppose that in a chi-squared goodness-of-fit test the unknown parameters are estimated from the likelihood of the continuous observations before grouping. The effect on the distribution of the test criterion is examined.

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正态多元系统维数显著性检验计算程序的代数理论AI 解读

Summary Before attempting to allot individuals to one of a set of normal multivariate populations, it is usual to make preliminary tests of significance to discover the structural relationships of the populations. In order to secure this reduction there are two separate methods, due to Fisher and (essentially) to Wilks. A simple algebraic proof is given for the identity of the statistics obtained from the two methods, and the condition under which Fisher’s method leads to…

关于循环多元分布的一则札记AI 解读

In Anderson's (1941) paper on the distribution of serial correlation coefficients, Hotelling's suggestion of a circular definition of these coefficients appears. Since then this device has been used constantly to lighten the mathematical difficulties in serial correlation theory. There has, however, been no suggestion that the model would ever be a good approximation in practice—the reverse has always been suggested in fact. It is the purpose of the present note to point out…

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