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平面标志点数据的形状变化AI 解读

This paper deals with the statistical analysis of matched pairs of shapes of configurations of landmarks in the plane. We provide inference procedures on the complex projective plane for a basic measure of shape change in the plane, on observing that shapes of configurations of $(k + 1)$ landmarks in the plane may be represented as points on $\mathbb{C} P^{k-1}$ and that complex rotations are the only maps on $\mathbb{C} S^{k-1}$ which preserve the usual Hermitian inner…

配对取向统计量的球面回归AI 解读

SUMMARY The matched pairs section of the analysis of 3 times 3 orientation statistics in Prentice (1986) may be improved on by constructing a rotational regression model, an analogue of spherical regression. The results obtained are relatively simple consequences of the work of Chang and are therefore presented here for general orientation statistics—rigid orthogonal m frames in p dimensions—before application to the matched pairs of vectorcardiogram orientations (m = p = 3)…

不依赖参数分布假设的取向统计AI 解读

SUMMARY Maximum likelihood estimation using the matrix von Mises-Fisher distribution in orientation statistics leads to unacceptably complicated likelihood equations, essentially because of the inconvenient form of the normalizing constant in the probability distribution. For the case of 3 × 2 or 3 × 3 orientations, the main cases of practical importance, an alternative approach is developed here by transforming the data into unsigned four-dimensional directions and using…

无符号方向数据的无分布区间估计方法AI 解读

A method of moments is suggested for large samples of unsigned directional data. The point estimators obtained coincide with the natural estimates obtained from maximum likelihood estimation if the data have a Bingham distribution. However, the calculations necessary for interval and regional estimation are considerably simpler. The statistical analysis is based upon the asymptotic sampling properties of principal components in nonnormal populations (Davis, 1977; Tyler,…

无符号方向数据的分布无关区间估计方法AI 解读

A method of moments is suggested for large samples of unsigned directional data. The point estimators obtained coincide with the natural estimates obtained from maximum likelihood estimation if the data have a Bingham distribution. However, the calculations necessary for interval and regional estimation are considerably simpler. The statistical analysis is based upon the asymptotic sampling properties of principal components in nonnormal populations (Davis, 1977; Tyler,…