Language Reference

References

Al-Baali, M. and Fletcher, R. (1985), "Variational Methods for Nonlinear Least Squares", J. Oper. Res. Soc., 36, 405 -421.
Al-Baali, M. and Fletcher, R. (1986), "An Efficient Line Search for Nonlinear Least Squares", J. Optimiz. Theory Appl., 48, 359 -377.
Ansley, C. (1979), "An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process," Biometrika, 66, 59 -65.
Bates, D., Lindstrom, M., Wahba, G. and Yandell, B. (1987), " GCVPACK-Routines for generalized Cross Validation," Comm. Statist. B-Simulation Comput., 16, 263 -297.
Barrodale, I. and Roberts, F.D.K. (1974), "Algorithm 478: Solution of an overdetermined system of equations in the l1-norm", Communications ACM, 17, 319 -320.
Beale, E.M.L. (1972), "A Derivation of Conjugate Gradients", in Numerical Methods for Nonlinear Optimization, ed. F. A. Lootsma (ed.), London: Academic Press.
Bishop, Y.M., Fienberg, S.E., and Holland, P.W. (1975), Discrete Multivariate Analysis: Theory and Practice, Cambridge, MA: MIT Press.
Box, G.E.P. and Jenkins, G.M. (1976), Time Series Analysis: Forecasting and Control, Oakland, CA: Holden-Day.
Bishop, Y.M., Fienberg, S.E., and Holland, P.W. (1975), Discrete Multivariate Analysis: Theory and Practice, Cambridge, MA: MIT Press.
Charnes, A., Frome, E.L., and Yu, P.L. (1976), "The Equivalence of Generalized Least Squares and Maximum Likelihood Estimation in the Exponential Family," Journal of the American Statistical Association, 71, 169 -172.
Cox, D.R. and Hinkley, D.V. (1974), Theoretical Statistics, London: Chapman and Hall.
De Jong, P. (1991b), "Stable algorithms for the state space model," it Journal of Time Series Analysis, 12, 143 -157.
Dennis, J.E., Gay, D.M., and Welsch, R.E. (1981), "An Adaptive Nonlinear Least-Squares Algorithm", ACM Trans. Math. Software, 7, 348 -368.
Dennis, J.E. and Mei, H.H.W. (1979), "Two new unconstrained optimization algorithms which use function and gradient values", J. Optim. Theory Appl., 28, 453 -482.
Duchon, J. (1976), "Fonctions-Spline et Esperances Conditionnelles de Champs Guassiens," in Ann. Sci. Univ. Clermont Ferrand II Math, 14, 19 -27.
Eskow, E. and Schnabel, R.B. (1991), "Algorithm 695: Software for a New Modified Cholesky Factorization", ACM Trans. Math. Software, 17, 306 -312.
Fletcher, R. (1987), Practical Methods of Optimization, 2nd Ed., Chichester: John Wiley & Sons.
Fletcher, R. and Xu, C. (1987), "Hybrid Methods for Nonlinear Least Squares", Journal of Numerical Analysis, 7, 371 -389.
Forsythe, G.E., Malcom, M.A., and Moler, C.B. (1967), Computer Solution of Linear Algebraic Systems, Chapter 17, Englewood Cliffs, NJ: Prentice-Hall, Inc.
Gay, D.M. (1983), "Subroutines for Unconstrained Minimization", ACM Trans. Math. Software, 9, 503 -524.
Golub, G.H., and Van Loan, C.F. (1989), Matrix Computations, 2nd Ed., Baltimore: J. Hopkins Univerity Press.
Gonin, R. and Money, A.H. (1989), Nonlinear L_p-norm Estimation, New York: M. Dekker, Inc.
Graybill, F.A. (1969), Introduction to Matrices with Applications in Statistics, Belmont, CA: Wadsworth, Inc.
Gentleman, W.M. and Sande, G. (1966), "Fast Fourier Transforms-for Fun and Profit," AFIPS Proceedings of the Fall Joint Computer Conference, 19, 563 -578.
George, J.A. and Liu, J.W. (1981), Computer Solution of Large Sparse Positive Definite Systems, New Jersey: Prentice-Hall.
Gill, E.P., Murray, W., Saunders, M.A., and Wright, M.H. (1984), "Procedures for Optimization Problems with a Mixture of Bounds and General Linear Constraints", ACM Trans. Math. Software, 10, 282 -298.
Goodnight, J.H. (1979) "A Tutorial on the SWEEP Operator," The American Statistician, 33, 149 -158.
Grizzle, J.E., Starmer, C.F., and Koch, G.G. (1969), "Analysis of Catagorical Data by Linear Models," Biometrics, 25, 489 -504.
Hadley, G. (1963), Linear Programming, Reading, MA: Addison-Wesley Publishing Company, Inc.
Harvey, A.C. (1989), Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge: Cambridge University Press.
Jenkins, M.A. and Traub, J.F. (1970), " A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration," SIAM Journal of Numerical Analysis, 7, 545 -566.
Jenrich, R.I. and Moore R.H. (1975), "Maximum Likelihood Estimation by Means of Nonlinear Least Squares," American Statistical Association, 1975 Proceedings of the Statistical Computing Section, 57 -65.
Kastenbaum, M.A. and Lamphiear, D.E. (1959), " Calculation of Chi-Square to Test the No Three-Factor Interaction Hypothesis," Biometrics, 15, 107 -122.
Kaiser, H.F. and Caffrey, J. (1965), "Alpha Factor Analysis," Psychometrika, 30, 1 -14.
Kruskal, J.B. (1964), "Nonmetric Multidimensional Scaling," Psychometrika, 29, 1-27, 115 -129.
Nelder, J.A. and Wedderburn, R.W.M. (1972), "Generalized Linear Models," Journal of the Royal Statistical Society, A.3, 370.
Lee, W. and Gentle, J.E. (1986), "The LAV Procedure", SUGI Supllememtal Library User's Guide, Cary: SAS Institute, Chapter 21, pp. 257 -260.
Lindstr $\ddot{o}$ m, P. and Wedin, P.A. (1984), "A new linesearch algorithm for nonlinear least-squares problems", Mathematical Programming, 29, 268 -296.
Madsen, K. and Nielsen, H.B. (1993), "A finite smoothing algorithm for linear l1 estimation", SIAM Journal on Optimization, 3, 223 -235.
McKean, J.W. and Schrader, R.M. (1987), "Least absolute errors analysis of variance", In: Y. Dodge, ed. Statistical Data Analysis - Based on L₁ Norm and Related Methods, Amsterdam: North Holland, 297 -305.
McLeod, I. (1975), "Derivation of the Theoretical Autocovariance Function of Autoregressive-Moving Average Time Series," Applied Statistics, 24, 255 -256.
Monro, D.M. and Branch, J.L. (1976), "Algorithm AS 117. The Chirp Discrete Fourier Transform and General Length," Applied Statistics, 26, 351 -361.
Mor $\acute{e}$ , J.J. (1978), "The Levenberg-Marquardt Algorithm: Implementation and Theory", in Lecture Notes in Mathematics 630, ed. G.A. Watson, Springer Verlag, Berlin-Heidelberg-New York, 105 -116.
Mor $\acute{e}$ , J.J. and Sorensen, D.C. (1983), "Computing a Trust-Region Step", SIAM J. Sci. Stat. Comput., 4, 553 -572.
Nussbaumer, H.J. (1982), Fast Fourier Transform and Convolution Algorithms, Second Edition, New York: Springer-Verlag.
Pizer, S.M. (1975), Numerical Computing and Mathematical Analysis, Chicago: Science Research Associates, Inc.
Powell, J.M.D. (1977), "Restart Procedures for the Conjugate Gradient Method", Mathematical Programming, 12, 241 -254.
Powell, J.M.D. (1978a), "A fast algorithm for nonlinearly constraint optimization calculations", in Numerical Analysis, Dundee 1977, Lecture Notes in Mathematics 630, ed. G.A. Watson, Springer Verlag, Berlin, 144 -175.
Powell, J.M.D. (1982b), "VMCWD: A Fortran subroutine for constrained optimization", DAMTP 1982/NA4, Cambridge, England.
Rao, C.R. and Mitra, S.K. (1971), Generalized Inverse of Matrices and its Applications, New York: John Wiley & Sons, Inc.
Reinsch, Christian H. (1967), "Smoothing by Spline Functions," Numerische Mahematik, 10, 177 -183.
Singleton, R.C. (1969), "An Algorithm for Computing the Mixed Radix Fast Fourier Transform," IEEE Transactions on Audio and Electoacoustics, AU-17, 93 -103.
Stoer, J. and Bulirsch, R. (1980), Introduction to Numerical Analysis, New York: Springer-Verlag.
Wahba, G. (1990), Spline Models for Observational Data, Philadelphia: Society for Industrial and Applied Mathematics.
Wilkinson, J.H. and Reinsch, C. (eds.), (1971), Linear Algebra, Handbook for Automatic Computation, Volume 2, New York: Sprringer-Verlag.
Woodfield, Terry J. (1988), "Simulating Stationary Gaussian ARMA Time Series," Computer Science and Statistics: Proceedings of the 20th Symposium on the Interface, 612 -617.
Young, F.W. (1981), "Quantitative Analysis of Qualitative Data," Psychometrika, 46, 357 -388.

Chapter Contents
Previous
Next
Top