Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis
By Alexander Shapiro. 1982
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Dimitris J. Bertsimas
- Rahul Mazumder
- Martin J. Wainwright
- J. F. Berge
- Venkat Chandrasekaran
- Francis R. Bach
- Martin S. Copenhaver
- Alan S. Willsky
Citations in the corpus
- The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability (2000, background): “(2.2) It is known (Ten Berge, Snijders & Zegers, 1981, lemma 2.4; Della Riccia & Shapiro, 1982, Theorem 4) that, for any Z, problem (2.1), and its equivalent (2.2), has a unique optimal solution, denoted subsequently by X̄ or X̄(Z).”
- Certifiably Optimal Low Rank Factor Analysis (2016, methodology): “Formulation of the estimator: In decomposition (1), the assumption that the rank ( r 1 ) of Σ c is small compared to p is fairly stringent, see Guttman (1958); Shapiro (1982); Ten-Berge (1998) for a historical overview of the concept.”
- Statistical inference of minimum rank factor analysis (2002, methodology): “The above derivations are similar to derivations related to MTFA presented in Shapiro and ten Berge (2000). Let us give a brief summary of the developed (asymptotic) statistical inference of the MRFA.”
- The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality (2004, background): “Shapiro (1982a) has proven that the minimal reduced rank will be at or above the Ledermann bound (Ledermann, 1937) almost surely.”
- Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting (2012, methodology): “Much of the basic analysis of MTFA, including optimality conditions and relations between minimum rank factor analysis and minimum trace factor analysis, was carried out in a sequence of papers by Shapiro [26, 27, 28] and Della Riccia and Shapiro [7].”