Mathematical programming for estimation of parameters in random blocks model

Parameter estimation is quite important in Statistics. Statisticians are engaged in various studies on this problem. Use of optimization methods in the solution of this estimation problem have become common especially after 1970's. The present study has the objective of estimating parameters in a random blocks design, completed random block design, balanced-incomplete random block design, and random block design in the case of a missing observation model equation capitalizing on the significance of optimization methods in statistics. In this study, minimum mean absolute deviations (MINMAD) method is defined and suggests the goal programming (GP) model for estimation of parameters in the random blocks model equation and compares the results obtained with those given by least squares method (LSM)

PDF

___

1.Narula, S. C., "Optimization Techniques in Linear Regression. A Review", TIMSS I Studies in Management Sciences, 19: 11-29 (1982)
2.Arthanari, T. S. and Dodge, Y., "Mathematical Programming in Statistic", John and Sons, New York, 304, 289- (1981)
3.Kligman, D. and Mote, J., "Generalized Network Approaches for Solving Least Absolute Value and Tchebycheef Regression Problems", TIMSS/Studies in Management Sciences, 19: 53-56 (1982)
4.Lee, C. K. and Ord, J. K., "Discriminate Analysis Using Least Absolute Deviations", Decisions Sciences, 21: 86-96 (1990)
5.Narula, S. C. and Korhenen, P. J. "Multivariate Multiple Linear Regression Based on Minimum Sum of Absolute Error Criterion", European Journal of Operation Research, 73(24): 70-75 (1994)
6. Eminkahyagil, G. and Apaydın, A., “The Goal Programming in Regression Analysis”, Bulletion of The International Statistical Institute, İstanbul, 51(2): 137-139 (1997)
7. Apaydın, A., “A Brunch, Boundary Algorithm In The Selection Of The Best Subset In Multiple Linear Regression”, Hacettepe Bulletin Of Natural Sciences and Engineering, 18: 175-192 (1997)
8. Dielman, T. and Pfaffenberger, R., “LAV (Least Absolute Value) Estimation in Linear Regression, A. Review”, TIMSS/Studies in Management Sciences, 19: 31-52 (1982)
9. Eminkahyagil, G., “Goal Programming and a Application, Bilim Uzmanlığı Tezi, Ankara Üniversitesi Fen Bilimleri Enstitüsü, Ankara, 34-51 (1997)
10. Charnes, A. Cooper, W. W., and Sueyoshi, T., “Least Squares/Ridge Regression and Goal Programming/Constrained Regression Alternatives”, European Journal of Operation Research, 27: 146-157 (1986)
11. Montgomery, D. C., “Design and Analysis of Experiments”, 4. Printed, John Wiley & Sons, New York, 171-194 (1997)
12. Montgomery, D. C., “Design and Analysis of Experiments”, 2. Printed, John Wiley & Sons, New York, 165-181 (1984)
13. Hosmand, A. Reaz., “Statistical Methods for Agricultural Sciences”, Timber Press, USA , 225-230 (1998)
14. Ott, L., “An Introduction to Statistical Methods and Data Analysis, PWS Pub. Co, USA, 656-659 (1988)