Linear regression estimators for multinormal distributions in optimization of stochastic programming problems

European Journal of Operational Research

Volumn 111, Issue 3, 1998, Pages 555-568

  Deák, István ^a,b  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Gradient of the normal distribution; Multinormal distribution; Probability constrained programming; Quantile problem; Regression estimators

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; DECISION THEORY; FUNCTIONS; NORMAL DISTRIBUTION; QUADRATIC PROGRAMMING; RANDOM PROCESSES;

LINEAR REGRESSION ESTIMATORS; PROBABILITY CONSTRAINED PROGRAMMING; STOCHASTIC PROGRAMMING;

REGRESSION ANALYSIS;

EID: 0042597809     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(97)00360-3     Document Type: Article

References (23)

1. P. Bjerager, On computation methods for structural reliability analysis, Structural Safety 9 (1990) 79-96.
2. J. A. Breslaw, Evaluation of multivariate normal probability integrals using low variance simulator, Review of Economic Statistics 76 (1994) 673-682.
3. I. Deák, Three digit accurate multiple normal probabilities, Numerische Mathematik 35 (1980) 369-380.
4. I. Deák, Computation of multiple normal probabilities, in: P. Kall, A. Prékopa (Eds.), Symposium on Stochastic Programming, Oberwolfach, Springer Lecture Notes in Economics and Math. Systems, vol. 179, Springer, Berlin, 1980, pp. 107-120.
5. I. Deák, Computing probabilities of rectangles in case of multidimensional normal distribution, Journal of Statistical Computation and Simulation 26 (1986) 101-114.
6. I. Deák, Procedures to solve STABIL on a parallel computer, Working Paper, University of Wisconsin, Department of Industrial Engineering, 89-10, lecture at the Vth International Conference on Stochastic Programming, Ann Arbor, MI, 1989, p. 26.
7. I. Deák, Random Number Generators and Simulation, in: A. Prékopa (Eds.), Mathematical methods of Operations Research, vol. 4, Akadémiai Kiadó, Budapest, 1990, p. 342.
8. I. Deák, Simple regression estimators for the multinormal distributions, Lecture at XIII International Conference on Operations Research, Mátraháza, 1996.
9. I. Deák, Approximations to the standard normal distribution function, Central European J. Oper. Res. and Econ. (submitted).
10. I. Deák, Regression estimators for multinormal distributions: computer experiences in root finding, in: K. Marti (Ed.), Proceedings of the Workshop in Stochastic Programming, Neubiberg, Springer, 1996 (submitted).
11. I. Deák, Asynchronous parallel models for optimization, in: Ljubljana, R. Trobec, M. Vajtersic, P. Zinterhof, J. Silc, B. Robic (Eds.), Proceedings of the ParNum96, International Workshop on Parallel Numerics, Slovenia, Gozd Martuljek, 1996, pp. 195-205.
12. O.J. Ditlevsen, P. Bjerager, Plastic reliability analysis by directional simulation, Journal of Engineering Mechanics 115 (1989) 1347-1362.
13. V. Ducroucq, J.J. Colleau, Interest in quantitative genetics of Dutt's and Deak's methods for numerical computation of multivariate normal probability integrals, Genetique, Selection et Evolution 18 (1986) 447-474.
14. H. Gassmann, Conditional probability and conditional expectation of a random vector, in: Y. Ermoliev, R. Wets (Eds.), Numerical techniques for stochastic optimization Springer series in computational mathematics, Springer, Berlin, 1988, pp. 237-254.
15. N.L. Johnson, S. Kotz, Distributions in Statistics, vols.I-IV, Wiley, New York, 1972.
16. P. Kail, A. Ruszczyński, K. Frauendorfer, Approximation techniques in stochastic programming, in: Y. Ermoliev, R. Wets (Eds.), Numerical techniques for stochastic optimization, Springer series in computational mathematics, 1988, pp. 33-64.
17. J. Mayer, Computational techniques for probabilistic constrained optimization problems, in: K. Marti (Ed.), Lecture Notes on Economics and Mathematical Systems, vol. 379 (1992), 141-164.
18. J. Mayer, Personal communication, 1996.
19. A. Prékopa, Boole-Bonferroni inequalities and linear programming, Operations Research 36 (1988) 145-162.
20. A. Prékopa, Stochastic Programming, Mathematics and its Applications, vol. 324, Kluwer Academic Publishers, Dordrecht, 1995.
21. A. Prékopa, S. Ganczer, I. Deák, K. Patyi, The STABIL stochastic programming model and its experimental application to the electrical energy sector of the Hungarian economy, in: M. Dempster (Ed.), Proceedings of the International Symposium on Stochastic Programming, Academic Press, New York, 1980, pp. 369-385.
22. A. Sen, M. Srivastava, Regression Analysis, Springer, Berlin, 1990.
23. T. Szántai, Evaluation of a special multivariate gamma distribution function, Mathematical Programming Study 27 (1986) 1-16.