Abstract
Basic numerical concepts, like cancellation, instability and condition number, are described and discussed. The implication on statistical computation is exemplified on computing variances and regression coefficients.
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References
Antoch, J. and Ekblom, H. (1994): Recursive Robust Regression - Computational Aspects and Comparison. To be published in Computational Statistics and Data Analysis.
Barrodale, I. and Roberts, F.D.K. (1973): An improved algorithm for discrete li linear approximation. SIAM J. Num. Anal. 10, 839–848.
Boéek, P. and Lachout, P. (1994): Linear programming approach to LMS-estimation. To be published in Computational Statistics and Data Analysis.
Byrd, R.H. and Pyne, D.A (1979): Convergence of the IRLS Algorithm for Robust Regression. Tech.Report No 313, Dept. of Math. Sciences, The John Hopkins University.
Chan, T., Golub, G. and Leveque, R. (1983): Algorithms for Computing the Sample Variance: Analysis and Recommendations. The American Statistician, 37(3).
Coleman, T.F. and Li, Y. (1992): A global and quadratically-convergent affine scaling method for linear ll problems, Math. Programming 56, 189–222.
Cox, D. (1992): The Role of the Computer in Statistics. In Proceedings of COMPSTAT 92, Y.Dodge and J.Whittaker, eds., Physica-Verlag.
Dahlquist, G. and Björk, A. (1974): Numerical Methods. Prentice-Hall, Englewood Cliffs, N.J.
Dongarra, J.J., Demmel, J.W. and Ostrouchov, S. (1992): LAPACK: A Linear Algebra Library for High Performance Computers. In Proceedings of COMPSTAT 92, Y.Dodge and J.Whittaker, eds., Physica-Verlag.
Dongarra, J.J and Grosse, E. (1987): Distribution of mathematical software via electronic mail. Comm ACM, 30(5), 403–407.
Dongarra, J.J. et al. (1990): A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Soft., 16(1), 1–17.
Edlund, O. (1994): A Study of Possible Speed-up when using a Vector Processor. Short communication, COMPSTAT 94.
Ekblom, H. and Madsen, K. (1989): Algorithms for non-linear Huber estimation, BIT 29, 60–76.
Fairbrother, R.W. (1987): The Historical Developement of the L1 and L, Estimation Procedures. In Dodge (ed): Statistical Data Analysis Based on the L1-Norm and Related Methods, North-Holland.
Fletcher, R. (1987): Practical Methods of Optimization. 2nd Edition, John Wiley.
Golub, G. and van Loan, C. (1989): Matrix Computations. John Hopkins University Press, Baltimore, MD, 2nd edition, 1989.
Hawkins, D.M. (1993): A feasable set algorithm for least median of squares regression. Computational Statistics and Data Analysis 16, 81–101
Huber, P.J. (1964): Robust Estimation of a Location Parameter. Annals of Mathematical Statistics 35, 73–101.
Huber, P.J. (1981): Robust Statistics. John Wiley, New York.
Kahaner, D., Moler, C. and Nash, S. (1989): Numerical Methods and Software. Prentice Hall, New Jersey.
Kennedy, W.J. and Gentle, J.E. (1980): Statistical Computing. Marcel Dekker, New York and Basel.
Prof. Georg Lindgren, University of Lund, Sweden, personal communication.
Madsen, K. and Nielsen, H.B. (1993): A finite smooting algorithm for linear estimation. SIAM J. Optimization, 3(2), 223–235.
O’Leary, D. (1990): Robust Regression Computation Using Iteratively Reweighted Least Squares. SIAM J. Matrix Anal. Appl., 11(3), 466–480.
Rice, J.R. and White, J.S. (1964): Norms for Smoothing and Estimation. SIAM Review 6, 243–256.
Stevenson, D. (1981): A Proposed Standard for Binary Floating Point Arithmetic. Computer 14, 51–62.
Strang, G. (1987): Karmarkar’s Algorithm and Its Place in Applied Mathematics. The Mathematical Intelligencer 9(2).
Watson, G.A. (1980): Approximation Theory and Numerical Methods. John Wiley, New York.
Xu, C.-W and Shiue, W.-K. (1993): Parallel algorithms for least median of squares regression. Computational Statistics and Data Analysis 16(3), 349–362.
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© 1994 Springer-Verlag Berlin Heidelberg
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Ekblom, H. (1994). What can Numerical Analysis do for Statistics?. In: Dutter, R., Grossmann, W. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-52463-9_3
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DOI: https://doi.org/10.1007/978-3-642-52463-9_3
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0793-6
Online ISBN: 978-3-642-52463-9
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