Covariance, Subspace, and Intrinsic CramrRao Bounds

By H. V. Trees, K. Bell. 2007

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A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank (2013, methodology): “We immediately get that W = 0 satisfies (5), as is known from Smith (2005). Next, we prove the case p < n by contradiction.”
Regression on Fixed-Rank Positive Semidefinite Matrices: A Riemannian Approach (2010, methodology): “(12) The affine-invariant geometry of S+(d) has been well studied, in particular in the context of information geometry [Smith, 2005].”
A Geometric Approach to Maximum Likelihood Estimation of the Functional Principal Components From Sparse Longitudinal Data (2007, methodology): “The first study is focussed on the estimation accuracy of the proposed method (henceforth, Newton) and comparing it with two existing procedures: the local polynomial method (henceforth, loc) [Yao et al. (2005)], and the EM algorithm (henceforth, EM) [James et al.”
Statistical eigen-inference from large Wishart matrices (2007, background): “See, for example, the text by Van Trees (2002) and the work of Smith (2005).”
Multiclass Brain–Computer Interface Classification by Riemannian Geometry (2012, background): “The SCM is known to be an unbiased estimator of the covariance matrix Σ provided that the number of observations Ts is much larger than the number of variables n [11].”
Stochastic Gradient Descent on Riemannian Manifolds (2011, unknown): “In [34], Smith has proposed an intrinsic”