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Improvement on the Best Invariant Estimators of the Normal Covariance and Precision Matrices via a Lower Triangular Subgroup

Hisayuki Tsukuma
2014 Journal of the Japan Statistical Society  
A commutator subgroup of lower triangular matrices is considered for deriving a class of invariant estimators.  ...  This paper addresses the problems of estimating the normal covariance and precision matrices.  ...  We considered a class of invariant estimators under the commutator subgroup of lower triangular matrices with positive diagonal entries.  ... 
doi:10.14490/jjss.44.195 fatcat:rnrk3n6ygbbhjawxvw4adfpv5q

Kernel Density Estimation on Symmetric Spaces [article]

Dena Marie Asta
2019 arXiv   pre-print
We construct and prove the existence of a kernel density estimator on symmetric spaces of non-compact type with minimax convergence rate.  ...  Symmetric spaces of non-compact type include hyperboloids of constant curvature -1 and spaces of symmetric positive definite matrices.  ...  triangular (2 × 2)matrices with 1's along the diagonal.  ... 
arXiv:1411.4040v2 fatcat:2dhhw2obuzffbhp5ikxz7vlzoy

Author index to volumes 41–60 (1981–1984)

1984 Linear Algebra and its Applications  
KARLIN, SAMUEL AND RINOT~, YOSEF: M-Matrices as Covariance Matrices of Multinormal Distributions, 52:419 (1983) KASZKUREWICZ, E.  ...  TANNENBAUM, ALLEN: On the Stabilizer Subgroup of a Pair of Matrices, 5Oz527 (1983) TAUSSKY, OLGA: On the Congruence Transformation of a Pencil of Real Symmetric Matrices to a Pencil with Identical Characteristic  ...  RAYKHSHTEYN, BORIS: On Rational Invariants of a Set of Symmetric Matrices, 54:17 (1983) RICE, JOHN R.: Performance Analysis of 13 Methods to Solve the Galerkin Method Equations, 52533 (1983) RIES,  ... 
doi:10.1016/0024-3795(84)90082-x fatcat:3ha77kk3gbffffyejkec22x5ae


1999 Linear Algebra and its Applications  
Lerer, Factorization of banded lower triangular in-®nite matrices 247 (1996) 347 Gohberg, I., M.A.  ...  of commutative matrices.  ...  ., Rotation and Lorentz transformations in 2´2 and 2´4 complex matrices and in polarized-light physics 254 (1997) 383 Nowicki, A., On the nonexistence of rational ®rst integrals for systems of linear dierential  ... 
doi:10.1016/s0024-3795(99)00243-8 fatcat:xz5sbc3lzngydobg3ln6xp2cum

The summer meeting in ann Arbor

J. W. T. Youngs
1955 Bulletin of the American Mathematical Society  
., the 17 ways of repeating a flat design, as on wallpaper) were discovered empirically by the Moors in their decoration of the Alhambra.  ...  The present paper gives an abstract definition for each group in terms of two, three, or four generators.  ...  For the multinomial estimation problem, the classical estimator is shown to be asymptotically minimax for a wide variety of weight functions.  ... 
doi:10.1090/s0002-9904-1955-09979-8 fatcat:4rmgfntcavcclkvmixl6xgqg34

Geometric Optimization Methods for Adaptive Filtering [article]

Steven Thomas Smith
2013 arXiv   pre-print
Several algorithms are presented and their convergence properties are analyzed employing the Riemannian structure of the manifold.  ...  A new point of view is offered for the constrained optimization problem. Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds.  ...  The goal is to estimate the principal invariant subspaces of R xx . Several of the covariance estimation techniques mentioned above use an averaging approach to compute an estimate of R xx .  ... 
arXiv:1305.1886v1 fatcat:q3vvafkqfjazndl4vvm2m5c4ba

Author index

1988 Linear Algebra and its Applications  
a commuting pair by tensor products, 3:355-357 (1970) roots of tournament matrices, 8:271-272 (1974) us OLIVEIBA, G.  ...  ,AFI~Y, THOMAS ].: Simultaneous triangularization of a pair of matrices whose commutator has rank two, 29:195-203 (1980) LAr~Y, THOMAS J.: The minimal dimension of maximal commutative subalgebras of full  ... 
doi:10.1016/0024-3795(88)90386-2 fatcat:vbli3cgvuzcrhhvjrow447hq2i

Hilbert geometry of the Siegel disk: The Siegel-Klein disk model [article]

Frank Nielsen
2020 arXiv   pre-print
We study the Hilbert geometry induced by the Siegel disk domain, an open bounded convex set of complex square matrices of operator norm strictly less than one.  ...  For example, we show how to approximate the smallest enclosing ball of a set of complex square matrices in the Siegel disk domains: We compare two generalizations of the iterative core-set algorithm of  ...  (195) This is a minimax optimization problem.  ... 
arXiv:2004.08160v5 fatcat:ncc6oluapjgo5dzhfnbzwjstjq

The annual meeting in Pittsburgh

R. D. Schafer, J. W. Green
1955 Bulletin of the American Mathematical Society  
Maurice Auslander: Commutator subgroup of free groups. Let F be a non-abelian free group, R a proper normal subgroup of F, and [R, R] the commutator subgroup of R.  ...  Further, the duals of the spaces X(&Gd are described, where &C 2 consists of all products Cic 2 , Ci£&, C2GC2. Essential use is made of the minimax theorem of H. Kneser-Ky Fan.  ... 
doi:10.1090/s0002-9904-1955-09897-5 fatcat:fgaeb7kifnd3tndgo7eecdeoju

Index: Volumes 21-30

1971 Proceedings of the American Mathematical Society  
IP 35P15 Estimation of eigenvalues, upper and lower bounds 35P20 Asymptotic distribution of eigenvalues and eigenfunctions 35P25 Scattering theory [See also 47A40.] 35P99 None of the above  ...  W. 1 H2 of the commutator subgroup of a knot group, 28 (1971), 319-320. 18H10 55A05 55A25 Summers, W.  ... 
doi:10.1090/s0002-9939-71-99972-2 fatcat:fh3qmht755dope6cfo3csgim2i

Collaborating institutions [chapter]

2016 The Financial System We Need  
by using matrices as the previously described.  ...  We deal with the Lie groups G n (with n ∈ N) formed by square upper-triangular matrices of order n and whose elements in the main diagonal are "1".  ...  Let us consider the series (f − u(t)), (t = 0, 1, 2...), each term is a estimation of the 'noise' signal, then it is reasonable that the stopping time maximizes the gaussianity of the (f − u(t)).  ... 
doi:10.18356/b4968a28-en fatcat:v75hvlhqebfglfsx7q4qwwlc34

Universal points in the asymptotic spectrum of tensors [article]

Matthias Christandl, Péter Vrana, Jeroen Zuiddam
2018 arXiv   pre-print
We construct for the first time a family of nontrivial universal spectral points over the complex numbers, using quantum entropy and covariants: the quantum functionals.  ...  tensor, a prime example of Strassen.  ...  Let U − n ⊆ GL(C n ) be the unipotent subgroup of lower triangular n × n matrices with ones on the diagonal. Let Y be the variety of complete (decreasing) flags in C n .  ... 
arXiv:1709.07851v3 fatcat:uhdm3wzqtza63bjfugsvjttlyy

Guaranteed Local Maximum Likelihood Detection of a Change Point in Nonparametric Logistic Regression

A. Vexler, G. Gurevich
2006 Communications in Statistics - Theory and Methods  
We establish lower bounds on the minimax risk in estimating the change-point and develop rate optimal estimation procedures.  ...  Noninformative priors are used for all competing models: no-change model, mean change model, covariance change model, and mean and covariance change model.  ...  The method is spatially adaptive and covariate selection is achieved by using splines of lower dimension than the data.  ... 
doi:10.1080/03610920500498923 fatcat:jxva2knaxvbpbfmovc7yfwwlhu

Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges [article]

Michael M. Bronstein, Joan Bruna, Taco Cohen, Petar Veličković
2021 arXiv   pre-print
While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying  ...  low-dimensionality and structure of the physical world.  ...  Acknowledgements This text represents a humble attempt to summarise and synthesise decades of existing knowledge in deep learning architectures, through the geometric lens of invariance and symmetry.  ... 
arXiv:2104.13478v2 fatcat:odbzfsau6bbwbhulc233cfsrom

Morse Spectra, Homology Measures and Parametric Packing Problems [article]

Misha Gromov
2017 arXiv   pre-print
Weyl kind of asymptotics of the Morse (co)homology spectra of the volume energy function on the spaces of cycles in balls.  ...  We suggest several mathematical counterparts to the idea of "effective degrees of freedom" and formulate specific questions, much of which are inspired by Larry Guth's results and ideas on the Hermann  ...  ∶ S 1 → S 2 , such that the corresponding triangular diagrams are (homotopy) commutative, i.e. the composed maps φ 2 ○ ϕ 12 ∶ S 1 → Ψ are homotopic to φ 1 .  ... 
arXiv:1710.03616v1 fatcat:v5cnjiamlvallnstu3o2w6mwg4
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