The ℓ1 oblique Procrustes problem

Statistics and Computing

Volumn 14, Issue 1, 2004, Pages 39-51

  Trendafilov, Nickolay T ^a   Watson, G A ^b  

^a UNIVERSITY OF THE WEST OF ENGLAND   (United Kingdom)

^b UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

Constrained optimization; Descent flows; Dynamical system on manifolds; Fitting configurations; Optimality conditions; Reference structure and factor pattern

Indexed keywords

EID: 3843091585     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:STCO.0000009415.14785.2a     Document Type: Article

References (30)

1. Barnett V. and Lewis T. 1978. Outliers in Statistical Data. John Wiley, Chichester.
2. 1 solution of an overdetermined linear system. SIAM Journal on Numerical Analysis 15: 224-241.
3. Benson H.Y. and Vanderbie R. 1999. Using LOQO to solve second order cone problems, Princeton University Technical Report 98-09, see also www.sor.princeton.edu/~rvdb/ps/socp.pdf.
4. Chu M.T. and Trendafilov N.T. 1998. On a differential equation approach to the weighted orthogonal Procrustes problem. Statistics and Computing 8: 125-133.
5. Chu M.T. and Trendafilov N.T. 2001. The orthogonally constrained regression revisited. Journal of Computational and Graphical Statistics 10(4): 1-26.
6. Clark D.I. 1985. The mathematical structure of Huber's-estimator. SIAM Journal on Scietific and Statistical Computing 6: 209-219.
7. Dryden I.L. and Mardia K.V. 1998. Statistical Shape Analysis. John Wiley & Sons, Chichester.
8. 1 Norm and Related Methods. North Holland, Amsterdam, pp. 37-63.
9. Farebrother R.W. 1999. Fitting Linear Relationships: A History of the Calculus of Observations 1750-1900. Springer-Verlag, Berlin.
10. Helmke U. and Moore J.B. 1994. Optimization and Dynamical Systems. Springer, London.
11. Hirsch M.W. and Smale S. 1974. Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, London.
12. Huber P.J. 1981. Robust Statistical Procedures. SIAM Regional Conference Series in Applied Mathematics, No 27.
13. Li W. and Swetits J.J. 1998. Linear (3)1 (estimator and Huber M-estimator. SIAM Journal on Optimization 8: 457-475.
14. Lobo M.S., Vandenberghe L., and Boyd S.P. 1998. SOCP: Primal dual potential reduction method for solving second-order cone programming problems, Stanford Report, see also www.stanford.edu/~boyd/SOCP.html.
15. 1 estimation. SIAM Journal on Optimization 3: 223-235.
16. 1 solutions to overdetermined systems of linear equations. Operation Research Letters 16: 159-166.
17. Magnus J.R. and Neudecker H. 1988. Matrix Differential Calculus with Applications in Statistics and Econometrics. John Wiley & Sons, New York.
18. Mulaik S. 1972. The Foundations of Factor Analysis. McGrow Hill, New York.
19. Osborne M.R., Presnell B., and Turlach B.A. 2000. On the LASSO and its dual. Journal Computational and Graphical Statistics 9: 319-337.
20. Portnoy S. and Koenker R. 1999. The Gaussian hare and the Laplacian tortoise: Computability of squares-error versus absolute-error estimators. Statistical Science 12: 279-300.
21. Rockafellar R.T. 1970. Convex Analysis. Princeton University Press, Princeton.
22. Rohlf F.J. and Slice D. 1990. Extensions of the Procrustes method for the optimal superimposition of landmarcs. Systematic Zoology 39(1): 40-59.
23. Rousseeuw P.J. and Leroy A.M. 1987. Robust Regression and Outlier Detection. John Wiley & Sons, New York.
24. Shampine L.F. and Reichelt M.W. 1997. The MATLAB ODE suite. SIAM Journal on Scientific Computing 18: 1-22.
25. Siegel A.F. and Benson R.H. 1982. A robust comparison of biological shapes. Biometrics 38: 341-350.
26. Siegel A.F. and Pinkerton J.R. 1982. Robust comparison of three-dimensional shapes with an application to protein molecule configurations. Technical Report # 217, Series 2, Department of Statistics, Princeton University.
27. Stigler S.M. 1986. The History of Statistics: The Measurement of Uncertainty before 1900. Harvard University Press, Cambridge, Massachusetts.
28. Sturm J. 2002. SEDUMI User's Guide. Department of Econometrics, Tilburg University, http://fewcal.kub.nl/ sturm/software/sedumi.html.
29. Trendafilov N.T. 1999. A continuous-time approach to the oblique Procrustes problem. Behaviormetrika 26(2): 167-181.
30. Verboon P. 1994. A Robust Approach to Nonlinear Multivariate Analysis. DSWO Press, Leiden.