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LaTeX/main.bib
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LaTeX/main.bib
@ -1,12 +1,16 @@
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@book{AbadirMagnus2005,
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author = {Abadir, Karim M. and Magnus, Jan R.},
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year = {2005},
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title = {Matrix Algebra},
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publisher = {Cambridge University Press},
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doi = {10.1017/CBO9780511810800},
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collection = {Econometric Exercises},
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place = {Cambridge},
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series = {Econometric Exercises}
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author = {Abadir, Karim M. and Magnus, Jan R.},
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year = {2005},
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title = {Matrix algebra},
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volume = {1},
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pages = {xxx+434},
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publisher = {Cambridge University Press, Cambridge},
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doi = {10.1017/CBO9780511810800},
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url = {https://doi.org/10.1017/CBO9780511810800},
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isbn = {978-0-521-53746-9; 0-521-53746-0},
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mrclass = {15-01 (91B02)},
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mrnumber = {2408356},
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series = {Econometric Exercises}
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}
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@book{AbsilEtAl2007,
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@ -47,15 +51,16 @@
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}
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@book{Arnold1981,
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author = {Arnold, Steven F},
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year = {1981},
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title = {The theory of linear models and multivariate analysis},
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publisher = {Wiley},
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address = {New York, NY [u.a.]},
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isbn = {0471050652},
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keywords = {Multivariate Analyse},
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language = {eng},
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series = {Wiley series in probability and mathematical statistics : Probability and mathematical statistics}
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author = {Arnold, Steven F.},
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year = {1981},
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title = {The theory of linear models and multivariate analysis},
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pages = {xvi+475},
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publisher = {John Wiley \& Sons, Inc., New York},
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isbn = {0-471-05065-2},
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mrclass = {62-01 (62J05)},
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mrnumber = {606011},
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mrreviewer = {Pi-Erh\ Lin},
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series = {Wiley Series in Probability and Mathematical Statistics}
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}
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@article{BanerjeeEtAl2008,
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@ -438,11 +443,19 @@
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}
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@book{Cook1998,
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author = {Cook, Dennis R.},
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year = {1998},
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title = {Regression Graphics: Ideas for studying regressions through graphics},
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publisher = {Wiley},
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address = {New York}
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author = {Cook, R. Dennis},
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year = {1998},
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title = {Regression graphics},
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pages = {xviii+349},
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publisher = {John Wiley \& Sons, Inc., New York},
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doi = {10.1002/9780470316931},
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url = {https://doi.org/10.1002/9780470316931},
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isbn = {0-471-19365-8},
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mrclass = {62-01 (62J05)},
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mrnumber = {1645673},
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mrreviewer = {Jon\ Stene},
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note = {Ideas for studying regressions through graphics, A Wiley-Interscience Publication},
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series = {Wiley Series in Probability and Statistics: Probability and Statistics}
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}
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@article{Cook2000,
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@ -590,17 +603,19 @@
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}
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@article{CoxWermuth1994,
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author = {D. R. Cox and Nanny Wermuth},
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year = {1994},
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title = {A Note on the Quadratic Exponential Binary Distribution},
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journal = {Biometrika},
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volume = {81},
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number = {2},
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pages = {403--408},
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publisher = {[Oxford University Press, Biometrika Trust]},
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issn = {00063444},
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url = {http://www.jstor.org/stable/2336971},
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urldate = {2024-04-11}
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author = {Cox, D. R. and Wermuth, Nanny},
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year = {1994},
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title = {A note on the quadratic exponential binary distribution},
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journal = {Biometrika},
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volume = {81},
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number = {2},
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pages = {403--408},
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issn = {0006-3444,1464-3510},
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doi = {10.1093/biomet/81.2.403},
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url = {https://doi.org/10.1093/biomet/81.2.403},
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fjournal = {Biometrika},
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mrclass = {62E15},
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mrnumber = {1294901}
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}
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@book{Dai2012,
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@ -721,11 +736,20 @@
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}
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@article{DrtonEtAl2020,
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author = {Mathias Drton and Satoshi Kuriki and Peter D. Hoff},
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year = {2020},
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title = {Existence and uniqueness of the Kronecker covariance MLE},
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journal = {The Annals of Statistics},
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url = {https://api.semanticscholar.org/CorpusID:212718000}
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author = {Drton, Mathias and Kuriki, Satoshi and Hoff, Peter},
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year = {2021},
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title = {Existence and uniqueness of the {K}ronecker covariance {MLE}},
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journal = {Ann. Statist.},
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volume = {49},
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number = {5},
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pages = {2721--2754},
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issn = {0090-5364,2168-8966},
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doi = {10.1214/21-aos2052},
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url = {https://doi.org/10.1214/21-aos2052},
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fjournal = {The Annals of Statistics},
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mrclass = {62H12 (62R01)},
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mrnumber = {4338381},
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mrreviewer = {Burcu\ H.\ Ucer}
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}
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@article{DrydenEtAl2009,
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@ -5,13 +5,9 @@
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\usepackage[utf8]{inputenc}
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\usepackage[LSF, T1]{fontenc}
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\usepackage{chessfss}
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% \usepackage{fullpage}
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\usepackage{amsmath, amssymb, amstext, amsthm, scalerel, bm, pifont}
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\usepackage[dvipsnames]{xcolor} % dvipsnames loads more named colors
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\usepackage{graphicx} % colors, images and graphics
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\usepackage{tikz} % TikZ (TeX ist kein Zeichenprogramm)
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\usepackage{environ} % for dynamic TikZ picture scaling
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\usepackage{algorithm, algpseudocode} % Pseudo Codes / Algorithms
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\usepackage[
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style = authoryear, % citation style
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isbn = false, % show isbn?
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@ -32,13 +28,9 @@
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doi = true,
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bibencoding = utf8
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]{biblatex}
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\usepackage[pdftex, colorlinks, allcolors=blue]{hyperref} % Load as last package! Redefines commands
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\usepackage[noabbrev, capitalize, nameinlink]{cleveref} % but this after hyperref
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\usetikzlibrary{calc, perspective, datavisualization}
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\setcounter{MaxMatrixCols}{20} % Sets the max nr. of columns in AMSmath's matrix envs to 20
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% Document meta into
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@ -119,21 +111,21 @@
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% \newcommand*{\ten}[1]{\mathcal{#1}}
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% \DeclareMathOperator{\sym}{sym}
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\renewcommand*{\vec}{\operatorname{vec}}
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\newcommand*{\unvec}{\operatorname{vec^{-1}}}
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\newcommand*{\reshape}[1]{\operatorname{reshape}_{#1}}
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% \newcommand*{\unvec}{\operatorname{vec^{-1}}}
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% \newcommand*{\reshape}[1]{\operatorname{reshape}_{#1}}
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\newcommand*{\vech}{\operatorname{vech}}
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\newcommand*{\rank}{\operatorname{rank}}
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\newcommand*{\diag}{\operatorname{diag}}
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\newcommand*{\perm}[1]{\mathfrak{S}_{#1}} % set of permutations of size #1
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\newcommand*{\len}[1]{\#{#1}} % length of #1
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\DeclareMathOperator*{\ttt}{\circledast}
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% \newcommand*{\perm}[1]{\mathfrak{S}_{#1}} % set of permutations of size #1
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% \newcommand*{\len}[1]{\#{#1}} % length of #1
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% \DeclareMathOperator*{\ttt}{\circledast}
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\DeclareMathOperator{\tr}{tr}
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\DeclareMathOperator{\var}{Var}
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\DeclareMathOperator{\cov}{Cov}
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\DeclareMathOperator{\Span}{span}
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\DeclareMathOperator{\E}{\operatorname{\mathbb{E}}}
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% \DeclareMathOperator{\independent}{{\bot\!\!\!\bot}}
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\DeclareMathOperator*{\argmin}{{arg\,min}}
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% \DeclareMathOperator*{\argmin}{{arg\,min}}
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\DeclareMathOperator*{\argmax}{{arg\,max}}
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\newcommand*{\D}{\textnormal{D}} % derivative
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\renewcommand*{\H}{\textnormal{H}} % hessian
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@ -146,21 +138,21 @@
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\renewcommand{\checkmark}{{\color{Green}\ding{51}}}
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\newcommand{\xmark}{{\color{Red!70}\ding{55}}}
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% Pseudo Code Commands
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\newcommand{\algorithmicbreak}{\textbf{break}}
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\newcommand{\Break}{\State \algorithmicbreak}
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% % Pseudo Code Commands
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% \newcommand{\algorithmicbreak}{\textbf{break}}
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% \newcommand{\Break}{\State \algorithmicbreak}
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% Special Matrix Sets (Manifolds)
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\newcommand{\MatMani}[2]{\mathbb{R}^{{#1}\times {#2}}}
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% \newcommand{\MatMani}[2]{\mathbb{R}^{{#1}\times {#2}}}
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\newcommand{\StiefelNonCompact}[2]{\mathbb{R}_{*}^{{#1}\times {#2}}}
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\newcommand{\Stiefel}[2]{\mathrm{St}^{{#1}\times {#2}}}
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\newcommand{\MatRankMani}[3]{\mathbb{R}_{\rank={#1}}^{{#2}\times {#3}}}
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\newcommand{\DiagZeroMat}[1]{\mathbb{R}_{\diag=0}^{{#1}\times {#1}}}
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% \newcommand{\MatRankMani}[3]{\mathbb{R}_{\rank={#1}}^{{#2}\times {#3}}}
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% \newcommand{\DiagZeroMat}[1]{\mathbb{R}_{\diag=0}^{{#1}\times {#1}}}
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\newcommand{\SymMat}[1]{\mathrm{Sym}^{{#1}\times {#1}}}
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\newcommand{\SkewSymMat}[1]{\mathrm{Skew}^{{#1}\times {#1}}}
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% \newcommand{\SkewSymMat}[1]{\mathrm{Skew}^{{#1}\times {#1}}}
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\newcommand{\SymPosDefMat}[1]{\mathrm{Sym}_{++}^{{#1}\times {#1}}}
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\newcommand{\SymDiagZeroMat}[1]{\mathrm{Sym}_{\diag=0}^{p\times p}}
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\newcommand{\SymBand}[2]{\mathrm{SymBand}^{{#1}\times {#1}}_{#2}}
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% \newcommand{\SymDiagZeroMat}[1]{\mathrm{Sym}_{\diag=0}^{p\times p}}
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% \newcommand{\SymBand}[2]{\mathrm{SymBand}^{{#1}\times {#1}}_{#2}}
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\newcommand{\OrthogonalGrp}[1]{\mathrm{O}(#1)}
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\newcommand{\SpecialOrthogonalGrp}[1]{\mathrm{SO}(#1)}
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@ -233,23 +225,6 @@
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\makeatother
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%%% Scaling TikZ pictures using the `environ' package
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% see: https://tex.stackexchange.com/questions/6388/how-to-scale-a-tikzpicture-to-textwidth
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\makeatletter
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\newsavebox{\measure@tikzpicture}
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\NewEnviron{scaletikzpicturetowidth}[1]{%
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\def\tikz@width{#1}%
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\def\tikzscale{1}\begin{lrbox}{\measure@tikzpicture}%
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\BODY
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\end{lrbox}%
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\pgfmathparse{#1/\wd\measure@tikzpicture}%
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\edef\tikzscale{\pgfmathresult}%
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\BODY
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}
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\makeatother
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\newcommand{\smoothFunc}[2][\infty]{{C^{#2}(#1)}}
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\newcommand{\localSmoothFunc}[3][\infty]{{C^{#3}_{#1}(#2)}}
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\newcommand{\tangentSpace}[2]{\ensuremath{T_{#1}{#2}}}
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@ -450,9 +425,7 @@ The reduction in vectorized form is $\vec\ten{R}(\ten{X})=\t{\mat{B}}\vec(\ten{X
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\begin{figure}
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\centering
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\begin{scaletikzpicturetowidth}{0.5\textwidth}
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\input{images/reduction.tex}
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\end{scaletikzpicturetowidth}
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\includegraphics{images/reduction.pdf}
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\caption{\label{fig:SDRvisual}Visual depiction of the sufficient reduction in \cref{thm:sdr}.}
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\end{figure}
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