Abstract
Linear regression is the most commonly applied procedure in statistics. This fact alone underscores the importance of solving linear least squares problems quickly and reliably. In addition, iteratively reweighted least squares lies at the heart of a host of other optimization algorithms in statistics. The current chapter features four different methods for solving linear least squares problems: sweeping, Cholesky decomposition, the modified GramSchmidt procedure, and orthogonalization by Householder reflections. Later we take up solution by the singular value decomposition.
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References
Dempster AP (1969) Continuous Multivariate Analysis. Addison-Wesley, Reading, MA
Golub GH, Van Loan CF (1996) Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore
Goodnight JH (1979) A tutorial on the SWEEP operator. Amer Statistician 33:149-158
Henrici P (1982) Essentials of Numerical Analysis with Pocket Calculator Demonstrations. Wiley, New York
Hubert L, Meulman J, Heiser W (2000) Two purposes for matrix factorization: a historical appraisal. SIAM Review 42:68-82
Jennrich RI (1977) Stepwise regression. Statistical Methods for Digital Computers. Enslein K, Ralston A, Wilf HS, editors, Wiley-Interscience, New York, pp 58-75
Kennedy WJ Jr, Gentle JE (1980) Statistical Computing. Marcel Dekker, New York
Little RJA, Rubin DB (1987) Statistical Analysis with Missing Data. Wiley, New York
Miller KS (1987) Some Eclectic Matrix Theory. Robert E Krieger Publishing, Malabar, FL
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, Cambridge
Seber GAF, Lee AJ (2003) Linear Regression Analysis, 2nd ed. Wiley, Hoboken, NJ
Stewart GW (1987) Afternotes on Numerical Analysis. SIAM, Philadelphia
Strang G (1986) Introduction to Applied Mathematics. Wellesley-Cambridge Press, Wellesley, MA
Thisted RA (1988) Elements of Statistical Computing. Chapman & Hall, New York
Trefethen LN, Bau D III (1997) Numerical Linear Algebra. SIAM, Philadelphia
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Lange, K. (2010). Linear Regression and Matrix Inversion. In: Numerical Analysis for Statisticians. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5945-4_7
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DOI: https://doi.org/10.1007/978-1-4419-5945-4_7
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