Applications of quadratic minimisation problems in statistics

Albers et al. (2010) [2] showed that the problem min x ( x − t ) ′ A ( x − t ) subject to x ′ B x + 2 b ′ x = k where A is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the...

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Published in	Journal of multivariate analysis Vol. 102; no. 3; pp. 714 - 722
Main Authors	Albers, C.J., Critchley, F., Gower, J.C.
Format	Journal Article
Language	English
Published	Amsterdam Elsevier Inc 01.03.2011 Elsevier Taylor & Francis LLC
Series	Journal of Multivariate Analysis
Subjects	Algebra Canonical analysis Canonical analysis Constraints Constrained regression Hardy-Weinberg Minimisation Optimal scaling Procrustes analysis Quadratic forms Ratios Reduced rank Splines Constrained regression Constraints Exact sciences and technology Hardy–Weinberg Linear inference, regression Mathematical problems Mathematics Minimisation Multivariate analysis Number theory Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Optimal scaling Optimization Probability and statistics Procrustes analysis Quadratic forms Quadratic programming Ratios Reduced rank Sciences and techniques of general use Splines Statistical methods Statistics Studies Minimisation 62P99 Splines Reduced rank Optimal scaling Canonical analysis Constrained regression Ratios Constraints Quadratic forms 12A63 15A21 Hardy–Weinberg Procrustes analysis Solution uniqueness Multivariate analysis Spline approximation Canonical form Numerical approximation Hardy-Weinberg Quadratic form Numerical linear algebra Statistical method Statistical regression Numerical analysis Condition number
Online Access	Get full text
ISSN	0047-259X 1095-7243
DOI	10.1016/j.jmva.2010.11.009

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Abstract	Albers et al. (2010) [2] showed that the problem min x ( x − t ) ′ A ( x − t ) subject to x ′ B x + 2 b ′ x = k where A is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the general problem that may all be handled within a general unifying methodology. These include non-trivial considerations that arise when (i) A and/or B are not of full rank and (ii) where B is indefinite. General canonical forms for A and B that underpin the minimisation methodology give insight into structure that informs understanding.
AbstractList	Albers et al. (2010) [2] showed that the problem min x ( x − t ) ′ A ( x − t ) subject to x ′ B x + 2 b ′ x = k where A is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the general problem that may all be handled within a general unifying methodology. These include non-trivial considerations that arise when (i) A and/or B are not of full rank and (ii) where B is indefinite. General canonical forms for A and B that underpin the minimisation methodology give insight into structure that informs understanding. Albers et al. (2010) [2] showed that the problem min(x)(x - t)'A(x - t) subject to x'Bx + 2b'x where A is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the general problem that may all be handled within a general unifying methodology. These include non-trivial considerations that arise when (i) A and/or B are not of full rank and (ii) where B is indefinite. General canonical forms for A and B that underpin the minimisation methodology give insight into structure that informs understanding. [PUBLICATION ABSTRACT] Albers et al. (2010) [2] showed that the problem subject to where is positive definite or positive semi-definite has a unique computable solution. Here, several statistical applications of this problem are shown to generate special cases of the general problem that may all be handled within a general unifying methodology. These include non-trivial considerations that arise when (i) and/or are not of full rank and (ii) where is indefinite. General canonical forms for and that underpin the minimisation methodology give insight into structure that informs understanding.
Author	Critchley, F. Gower, J.C. Albers, C.J.
Author_xml	– sequence: 1 givenname: C.J. surname: Albers fullname: Albers, C.J. email: c.j.albers@rug.nl organization: Psychometrics and Statistical Methods, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, The Netherlands – sequence: 2 givenname: F. surname: Critchley fullname: Critchley, F. organization: Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK – sequence: 3 givenname: J.C. surname: Gower fullname: Gower, J.C. organization: Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
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Keywords	Minimisation 62P99 Splines Reduced rank Optimal scaling Canonical analysis Constrained regression Ratios Constraints Quadratic forms 12A63 15A21 Hardy–Weinberg Procrustes analysis Solution uniqueness Multivariate analysis Spline approximation Canonical form Numerical approximation Hardy-Weinberg Quadratic form Numerical linear algebra Statistical method Statistical regression Numerical analysis Condition number
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References	Newcomb (br000105) 1961; 19 Critchley, Marriott, Salmon (br000035) 1996; 64 Guttman (br000075) 1941; vol. 48 ten Berge (br000125) 1983; 48 Mertens (br000100) 1998; 47 Albers, Critchley, Gower (br000010) 2011; 102 Uhlig (br000140) 1979; 25 Gregory, Veall (br000070) 1985; 53 Fisher (br000045) 1938 Gower, Dijksterhuis (br000060) 2004; vol. 30 de Leeuw (br000040) 1982; 47 Lafontaine, White (br000090) 1986; 21 Green, Silverman (br000065) 1994; vol. 58 Cramer (br000030) 1974; 39 Browne (br000025) 1967; 32 Gower (br000050) 1998; 17 J.C. Gower, C.J. Albers, Between-group metrics (submitted for publication). Reinsch (br000115) 1967; 10 McDonald, Torii, Nishisato (br000095) 1979; 44 ten Berge, Nevels (br000135) 1977; 42 Krzanowski, Jonathan, McCarthy, Thomas (br000085) 1995; 44 Takane, Young, de Leeuw (br000120) 1977; 42 Rao, Mitra (br000110) 1971 Albers, Gower (br000020) 2010; 4 ten Berge, Kiers, Commandeur (br000130) 1993; 46 Healy, Goldstein (br000080) 1976; 63 C.J. Albers, J.C. Gower, Canonical Analysis, Ranks, Ratios & Fits (submitted for publication). Albers (br000005) 2008 Albers (10.1016/j.jmva.2010.11.009_br000010) 2011; 102 Mertens (10.1016/j.jmva.2010.11.009_br000100) 1998; 47 Albers (10.1016/j.jmva.2010.11.009_br000005) 2008 Browne (10.1016/j.jmva.2010.11.009_br000025) 1967; 32 ten Berge (10.1016/j.jmva.2010.11.009_br000125) 1983; 48 Green (10.1016/j.jmva.2010.11.009_br000065) 1994; vol. 58 ten Berge (10.1016/j.jmva.2010.11.009_br000130) 1993; 46 Takane (10.1016/j.jmva.2010.11.009_br000120) 1977; 42 Fisher (10.1016/j.jmva.2010.11.009_br000045) 1938 McDonald (10.1016/j.jmva.2010.11.009_br000095) 1979; 44 Healy (10.1016/j.jmva.2010.11.009_br000080) 1976; 63 Newcomb (10.1016/j.jmva.2010.11.009_br000105) 1961; 19 Gower (10.1016/j.jmva.2010.11.009_br000060) 2004; vol. 30 Reinsch (10.1016/j.jmva.2010.11.009_br000115) 1967; 10 Guttman (10.1016/j.jmva.2010.11.009_br000075) 1941; vol. 48 10.1016/j.jmva.2010.11.009_br000015 de Leeuw (10.1016/j.jmva.2010.11.009_br000040) 1982; 47 Albers (10.1016/j.jmva.2010.11.009_br000020) 2010; 4 10.1016/j.jmva.2010.11.009_br000055 Gower (10.1016/j.jmva.2010.11.009_br000050) 1998; 17 Rao (10.1016/j.jmva.2010.11.009_br000110) 1971 ten Berge (10.1016/j.jmva.2010.11.009_br000135) 1977; 42 Gregory (10.1016/j.jmva.2010.11.009_br000070) 1985; 53 Critchley (10.1016/j.jmva.2010.11.009_br000035) 1996; 64 Krzanowski (10.1016/j.jmva.2010.11.009_br000085) 1995; 44 Lafontaine (10.1016/j.jmva.2010.11.009_br000090) 1986; 21 Cramer (10.1016/j.jmva.2010.11.009_br000030) 1974; 39 Uhlig (10.1016/j.jmva.2010.11.009_br000140) 1979; 25
References_xml	– reference: J.C. Gower, C.J. Albers, Between-group metrics (submitted for publication). – volume: 32 start-page: 125 year: 1967 end-page: 132 ident: br000025 article-title: On oblique Procrustes rotation publication-title: Psychometrika – reference: C.J. Albers, J.C. Gower, Canonical Analysis, Ranks, Ratios & Fits (submitted for publication). – year: 1971 ident: br000110 article-title: Generalized Inverse of Matrices and its Applications – volume: 10 start-page: 177 year: 1967 end-page: 183 ident: br000115 article-title: Smoothing by spline functions publication-title: Numerische Mathematik – volume: 19 start-page: 144 year: 1961 end-page: 146 ident: br000105 article-title: On the simultaneous diagonalization of two semi-definite matrices publication-title: Quarterly Journal of Applied Mathematics – volume: vol. 48 start-page: 319 year: 1941 end-page: 348 ident: br000075 article-title: The quantifcation of a class of attributes: a theory and method of scale construction publication-title: The Prediction of Personal Adjustment – volume: 21 start-page: 35 year: 1986 end-page: 40 ident: br000090 article-title: Obtaining any Wald statistic you want publication-title: Economics Letters – volume: 102 start-page: 698 year: 2011 end-page: 713 ident: br000010 article-title: Quadratic minimisation problems in statistics publication-title: Journal of Multivariate Analysis – volume: 39 start-page: 139 year: 1974 end-page: 163 ident: br000030 article-title: On Browne’s solution for oblique Procrustes rotation publication-title: Psychometrika – year: 1938 ident: br000045 article-title: Statistical Methods for Research Workers – volume: 42 start-page: 593 year: 1977 end-page: 600 ident: br000135 article-title: A general solution for Mosier’s oblique Procrustes problem publication-title: Psychometrika – volume: 48 start-page: 631 year: 1983 end-page: 638 ident: br000125 article-title: A generalization of Verhelst’s solution for a constrained regression problem in ALSCAL and related MDS-algorithms publication-title: Psychometrika – volume: 4 start-page: 223 year: 2010 end-page: 237 ident: br000020 article-title: A general approach to handling missing values in Procrustes analysis publication-title: Advances in Data Analysis and Classification – volume: 44 start-page: 101 year: 1995 end-page: 115 ident: br000085 article-title: Discriminant analysis with singular covariance matrices: methods and applications to spectroscopic data publication-title: Journal of the Royal Statistical Society. Series C – volume: 42 start-page: 7 year: 1977 end-page: 67 ident: br000120 article-title: Nonmetric individual differences multidimensional scaling: an alternating least-squares method with optimal scaling features publication-title: Psychometrika – year: 2008 ident: br000005 article-title: Some quadratic optimisation problems in psychometrics publication-title: New Trends in Psychometrics – volume: 63 start-page: 219 year: 1976 end-page: 229 ident: br000080 article-title: An approach to the scaling of categorical attributes publication-title: Biometrika – volume: vol. 30 year: 2004 ident: br000060 publication-title: Procrustes Problems – volume: 64 start-page: 1213 year: 1996 end-page: 1222 ident: br000035 article-title: On the differential geometry of the Wald test with nonlinear restrictions publication-title: Econometrica – volume: vol. 58 year: 1994 ident: br000065 publication-title: Nonparametric Regression and Generalized Linear Models—a Roughness Penalty Approach – volume: 44 start-page: 211 year: 1979 end-page: 227 ident: br000095 article-title: Some results on proper eigenvalues and eigenvectors with applications to scaling publication-title: Psychometrika – volume: 25 start-page: 219 year: 1979 end-page: 237 ident: br000140 article-title: A recurring theorem about pairs of quadratic forms and extensions: a survey publication-title: Linear Algebra and its Applications – volume: 47 start-page: 87 year: 1982 end-page: 93 ident: br000040 article-title: Generalized eigenvalue problems with positive semidefinite matrices publication-title: Psychometrika – volume: 47 start-page: 527 year: 1998 end-page: 542 ident: br000100 article-title: Exact principal component influence measures applied to the analysis of spectroscopic data on rice publication-title: Applied Statistics – volume: 17 start-page: 2709 year: 1998 end-page: 2721 ident: br000050 article-title: The role of constraints in determining optimal scores publication-title: Statistics in Medicine – volume: 46 start-page: 119 year: 1993 end-page: 134 ident: br000130 article-title: Orthogonal Procrustes rotation for matrices with missing values publication-title: British Journal of Mathematical and Statistical Psychology – volume: 53 start-page: 1465 year: 1985 end-page: 1468 ident: br000070 article-title: Formulating Wald test of nonlinear restrictions publication-title: Econometrica – year: 1938 ident: 10.1016/j.jmva.2010.11.009_br000045 – volume: 44 start-page: 211 year: 1979 ident: 10.1016/j.jmva.2010.11.009_br000095 article-title: Some results on proper eigenvalues and eigenvectors with applications to scaling publication-title: Psychometrika doi: 10.1007/BF02293972 – volume: 10 start-page: 177 year: 1967 ident: 10.1016/j.jmva.2010.11.009_br000115 article-title: Smoothing by spline functions publication-title: Numerische Mathematik doi: 10.1007/BF02162161 – volume: 25 start-page: 219 year: 1979 ident: 10.1016/j.jmva.2010.11.009_br000140 article-title: A recurring theorem about pairs of quadratic forms and extensions: a survey publication-title: Linear Algebra and its Applications doi: 10.1016/0024-3795(79)90020-X – volume: 64 start-page: 1213 year: 1996 ident: 10.1016/j.jmva.2010.11.009_br000035 article-title: On the differential geometry of the Wald test with nonlinear restrictions publication-title: Econometrica doi: 10.2307/2171963 – year: 1971 ident: 10.1016/j.jmva.2010.11.009_br000110 – volume: 47 start-page: 527 issue: 4 year: 1998 ident: 10.1016/j.jmva.2010.11.009_br000100 article-title: Exact principal component influence measures applied to the analysis of spectroscopic data on rice publication-title: Applied Statistics – volume: 32 start-page: 125 year: 1967 ident: 10.1016/j.jmva.2010.11.009_br000025 article-title: On oblique Procrustes rotation publication-title: Psychometrika doi: 10.1007/BF02289420 – volume: vol. 30 year: 2004 ident: 10.1016/j.jmva.2010.11.009_br000060 – volume: 19 start-page: 144 year: 1961 ident: 10.1016/j.jmva.2010.11.009_br000105 article-title: On the simultaneous diagonalization of two semi-definite matrices publication-title: Quarterly Journal of Applied Mathematics doi: 10.1090/qam/124336 – volume: 63 start-page: 219 year: 1976 ident: 10.1016/j.jmva.2010.11.009_br000080 article-title: An approach to the scaling of categorical attributes publication-title: Biometrika doi: 10.1093/biomet/63.2.219 – volume: 46 start-page: 119 year: 1993 ident: 10.1016/j.jmva.2010.11.009_br000130 article-title: Orthogonal Procrustes rotation for matrices with missing values publication-title: British Journal of Mathematical and Statistical Psychology doi: 10.1111/j.2044-8317.1993.tb01005.x – volume: 39 start-page: 139 year: 1974 ident: 10.1016/j.jmva.2010.11.009_br000030 article-title: On Browne’s solution for oblique Procrustes rotation publication-title: Psychometrika doi: 10.1007/BF02291466 – volume: 44 start-page: 101 year: 1995 ident: 10.1016/j.jmva.2010.11.009_br000085 article-title: Discriminant analysis with singular covariance matrices: methods and applications to spectroscopic data publication-title: Journal of the Royal Statistical Society. Series C – volume: 4 start-page: 223 issue: 4 year: 2010 ident: 10.1016/j.jmva.2010.11.009_br000020 article-title: A general approach to handling missing values in Procrustes analysis publication-title: Advances in Data Analysis and Classification doi: 10.1007/s11634-010-0077-0 – volume: vol. 58 year: 1994 ident: 10.1016/j.jmva.2010.11.009_br000065 – volume: vol. 48 start-page: 319 year: 1941 ident: 10.1016/j.jmva.2010.11.009_br000075 article-title: The quantifcation of a class of attributes: a theory and method of scale construction – volume: 102 start-page: 698 issue: 3 year: 2011 ident: 10.1016/j.jmva.2010.11.009_br000010 article-title: Quadratic minimisation problems in statistics publication-title: Journal of Multivariate Analysis doi: 10.1016/j.jmva.2009.12.018 – volume: 47 start-page: 87 year: 1982 ident: 10.1016/j.jmva.2010.11.009_br000040 article-title: Generalized eigenvalue problems with positive semidefinite matrices publication-title: Psychometrika doi: 10.1007/BF02293853 – volume: 21 start-page: 35 issue: 1 year: 1986 ident: 10.1016/j.jmva.2010.11.009_br000090 article-title: Obtaining any Wald statistic you want publication-title: Economics Letters doi: 10.1016/0165-1765(86)90117-5 – volume: 17 start-page: 2709 issue: 23 year: 1998 ident: 10.1016/j.jmva.2010.11.009_br000050 article-title: The role of constraints in determining optimal scores publication-title: Statistics in Medicine doi: 10.1002/(SICI)1097-0258(19981215)17:23<2709::AID-SIM37>3.0.CO;2-8 – year: 2008 ident: 10.1016/j.jmva.2010.11.009_br000005 article-title: Some quadratic optimisation problems in psychometrics – volume: 48 start-page: 631 issue: 4 year: 1983 ident: 10.1016/j.jmva.2010.11.009_br000125 article-title: A generalization of Verhelst’s solution for a constrained regression problem in ALSCAL and related MDS-algorithms publication-title: Psychometrika doi: 10.1007/BF02293886 – volume: 42 start-page: 7 year: 1977 ident: 10.1016/j.jmva.2010.11.009_br000120 article-title: Nonmetric individual differences multidimensional scaling: an alternating least-squares method with optimal scaling features publication-title: Psychometrika doi: 10.1007/BF02293745 – volume: 53 start-page: 1465 issue: 6 year: 1985 ident: 10.1016/j.jmva.2010.11.009_br000070 article-title: Formulating Wald test of nonlinear restrictions publication-title: Econometrica doi: 10.2307/1913221 – ident: 10.1016/j.jmva.2010.11.009_br000015 – ident: 10.1016/j.jmva.2010.11.009_br000055 – volume: 42 start-page: 593 year: 1977 ident: 10.1016/j.jmva.2010.11.009_br000135 article-title: A general solution for Mosier’s oblique Procrustes problem publication-title: Psychometrika doi: 10.1007/BF02295981
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Snippet	Albers et al. (2010) [2] showed that the problem min x ( x − t ) ′ A ( x − t ) subject to x ′ B x + 2 b ′ x = k where A is positive definite or positive... Albers et al. (2010) [2] showed that the problem subject to where is positive definite or positive semi-definite has a unique computable solution. Here,... Albers et al. (2010) [2] showed that the problem min(x)(x - t)'A(x - t) subject to x'Bx + 2b'x where A is positive definite or positive semi-definite has a...
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SubjectTerms	Algebra Canonical analysis Canonical analysis Constraints Constrained regression Hardy-Weinberg Minimisation Optimal scaling Procrustes analysis Quadratic forms Ratios Reduced rank Splines Constrained regression Constraints Exact sciences and technology Hardy–Weinberg Linear inference, regression Mathematical problems Mathematics Minimisation Multivariate analysis Number theory Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Optimal scaling Optimization Probability and statistics Procrustes analysis Quadratic forms Quadratic programming Ratios Reduced rank Sciences and techniques of general use Splines Statistical methods Statistics Studies
Title	Applications of quadratic minimisation problems in statistics
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