ArticleInternational statistical review = Revue internationale de statistique2016
Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices.
Article in International statistical review = Revue internationale de statistique, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- Bayesian estimation of covariate assisted principal regression for brain functional connectivity.Biostatistics (Oxford, England) · 2025Article
- Bayesian scalar-on-network regression with applications to brain functional connectivity.Biometrics · 2025Article
- An Empirical Bayes Approach to Shrinkage Estimation on the Manifold of Symmetric Positive-Definite Matrices.Journal of the American Statistical Association · 2024Article
- Geostatistical modeling of positive-definite matrices: An application to diffusion tensor imaging.Biometrics · 2022Article
- Article
- Geodesic Lagrangian Monte Carlo over the space of positive definite matrices: with application to Bayesian spectral density estimation.Journal of statistical computation and simulation · 2018Article
- How Can Single Sensory Neurons Predict Behavior?Neuron · 2015Article
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Abstract
This article gives a formal definition of a lognormal family of probability distributions on the set of symmetric positive definite (SPD) matrices, seen as a matrix-variate extension of the univariate lognormal family of distributions. Two forms of this distribution are obtained as the large sample limiting distribution via the central limit theorem of two types of geometric averages of i.i.d. SPD matrices: the log-Euclidean average and the canonical geometric average. These averages correspond to two different geometries imposed on the set of SPD matrices. The limiting distributions of these averages are used to provide large-sample confidence regions and two-sample tests for the corresponding population means. The methods are illustrated on a voxelwise analysis of diffusion tensor imaging data, permitting a comparison between the various average types from the point of view of their sampling variability.
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