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平均刚体运动的估计AI 解读

This paper investigates the definition and the estimation of the Fréchet mean of a random rigid body motion in ℝp. The sample space SE(p) contains objects M=(R,t) where R is a p×p rotation matrix and t is a p×1 translation vector. This work is motivated by applications in biomechanics where the posture of a joint at a given time is expressed as M∈SE(3), the rigid body displacement needed to map a system of axes on one segment of the joint to a similar system on the other…

三维运动统计分析的方向模型AI 解读

Movement of an object in three dimensions involves rotation and translation. The data for analysis are the coordinates of landmarks on the object, recorded at several time points. Statistical models for describing the rotational component of the movement of an object are proposed in this work. Under the fixed‐axis model, the object rotates around an axis that does not change in time. The angular position of the object is then characterised by its rotation axis and an angle…

多元分布族依赖参数的半参数估计程序AI 解读

This paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions. The proposed estimator, obtained as a solution of a pseudo-likelihood equation, is shown to be consistent, asymptotically normal and fully efficient at independence. A natural estimator of its asymptotic variance is proved to be consistent. Comparisons are made with alternative semiparametric estimators in the special case of…