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Year 2006, Volume: 19 Issue: 1, 41 - 48, 24.03.2010

Abstract

References

  • Narula, S. C., “Optimization Techniques in Linear Regression. A Review”, TIMSS / Studies in Management Sciences, 19: 11-29 (1982)
  • Arthanari, T. S. and Dodge, Y., “Mathematical Programming in Statistic”, John and Sons, New York, 304, 289- (1981)
  • Kligman, D. and Mote, J., “Generalized Network Approaches for Solving Least Absolute Value and Tchebycheef Regression Problems”, TIMSS/Studies in Management Sciences, 19: 53- (1982)
  • Lee, C. K. and Ord, J. K., “Discriminate Analysis Using Least Absolute Deviations”, Decisions Sciences, 21: 86-96 (1990)
  • 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)
  • Eminkahyagil, G. and Apaydın, A., “The Goal Programming in Regression Analysis”, Bulletion of The International Statistical Institute, İstanbul, (2): 137-139 (1997)
  • 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)
  • Dielman, T. and Pfaffenberger, R., “LAV (Least Absolute Value) Estimation in Linear Regression, A. Review”, TIMSS/Studies in Management Sciences, 19: 31-52 (1982)
  • Eminkahyagil, G., “Goal Programming and a Application, Bilim Uzmanlığı Tezi, Ankara Üniversitesi Fen Bilimleri Enstitüsü, Ankara, 34- (1997)
  • 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)
  • Montgomery, D. C., “Design and Analysis of 9.7 Y. j Experiments”, 4. Printed, John Wiley & Sons, New York, 171-194 (1997)
  • Montgomery, D. C., “Design and Analysis of Experiments”, 2. Printed, John Wiley & Sons, New York, 165-181 (1984)
  • Hosmand, A. Reaz., “Statistical Methods for Agricultural Sciences”, Timber Press, USA , 225- (1998)
  • Ott, L., “An Introduction to Statistical Methods and Data Analysis, PWS Pub. Co, USA, 656-659 (1988) APPENDIX
  • A-) Problems used to estimate completed random block design parameters. Problem 1 (Artificial Data) Treatment 2 3 4 05 0.03 0.06 0.01 i 15 09 0 01 0.05 0 0.04 0.1 06 0.01 0.04 0 12 0.13 0.13 0.07 11 45 Y. j 0.06 065 07 26 07 0.075 0.07 0.065 0.28 067 0.072 0.069 0.060 0.268 197 0.212 0.204 0.195 0.808 j Problem 3 (Artificial Data) Treatment 2 3 4 i 21 19 20 78 17 19 19 71 23 20 24 86 61 58 63 235 j Problem 4 (Montgomery 1997) Treatment 2 3 4 4 i 3 9.3 6 4 9.3 9.8 9.9 38.4 2 9.4 9.5 9.7 37.8 6 2 5 6 37.7 38.9 39.8 154
  • Problem 5 (Artificial Data) Treatment 2 3 4 4 5 9.2 3 9.2 Y 9.2 3 4 5 37 5 8 37.2 37 37.1 148.1 j B-) Problems used to estimate balanced-incomplete random block design estimated parameters. Problem 1 (Artificial Data) Treatment 2 3 4 8 5 i 10.65 6 25 3 Y. j 5 25 3.55 5 3 8 55 10.55 11.3 11.4 Problem 2 (Artificial Data) Treatment 2 3 4 Y.ii 7.6 3 3 3.5 Y 6 2 4 8 5 10 4.4 4.8 29.7 7 j Problem 3 (Montgomery 1997) Treatment 2 3 4 75 68 - 72 75 222 224 207 218 i 218 214 Y. j
  • Problem 3 (Artificial Data) Treatment 2 3 4 4 5 9.2 3 6+y 9.2 Y 9.2 3 4 y 5 8 37.2 37 27.6+y 148.1 j 4 1 1 0 Y. j 5 4 4 8 2 1 y-2 -13 y-12 Problem 5 (Montgomery 1997) Treatment 2 3 4 1 2 1 5 2 Y 5 3 y 2 j
  • D-) Problems used to estimate random block design parameters in the case of two missing observations. Problem 1 (Montgomery 1997) Treat ment i 9.3 9.4 9.6 y 3 y1 + 9.4 9.3 9.8 9.9 9.2 9.4 9.5 9.7 9.7 9.6 10 y 4 8 Y. j 6 37.7 38.9 Block 2 3 4 Y.ii 0.05 0.03 0.06 0 0.04 0.03 0.01 y 01 0.15 02 0.09 0.04 0.05 y + y2 01 0.04 0 Y. j + 06 y2 08+ y1 13 0.07 0.34 y +

Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review)

Year 2006, Volume: 19 Issue: 1, 41 - 48, 24.03.2010

Abstract

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)

 

Keywords: MINMAD, Goal Programming, Randomize Block Design, Completed Random Block Design, Balanced-incomplete  Random Block Design, Random Block Design in Case of a Missing Observation

References

  • Narula, S. C., “Optimization Techniques in Linear Regression. A Review”, TIMSS / Studies in Management Sciences, 19: 11-29 (1982)
  • Arthanari, T. S. and Dodge, Y., “Mathematical Programming in Statistic”, John and Sons, New York, 304, 289- (1981)
  • Kligman, D. and Mote, J., “Generalized Network Approaches for Solving Least Absolute Value and Tchebycheef Regression Problems”, TIMSS/Studies in Management Sciences, 19: 53- (1982)
  • Lee, C. K. and Ord, J. K., “Discriminate Analysis Using Least Absolute Deviations”, Decisions Sciences, 21: 86-96 (1990)
  • 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)
  • Eminkahyagil, G. and Apaydın, A., “The Goal Programming in Regression Analysis”, Bulletion of The International Statistical Institute, İstanbul, (2): 137-139 (1997)
  • 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)
  • Dielman, T. and Pfaffenberger, R., “LAV (Least Absolute Value) Estimation in Linear Regression, A. Review”, TIMSS/Studies in Management Sciences, 19: 31-52 (1982)
  • Eminkahyagil, G., “Goal Programming and a Application, Bilim Uzmanlığı Tezi, Ankara Üniversitesi Fen Bilimleri Enstitüsü, Ankara, 34- (1997)
  • 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)
  • Montgomery, D. C., “Design and Analysis of 9.7 Y. j Experiments”, 4. Printed, John Wiley & Sons, New York, 171-194 (1997)
  • Montgomery, D. C., “Design and Analysis of Experiments”, 2. Printed, John Wiley & Sons, New York, 165-181 (1984)
  • Hosmand, A. Reaz., “Statistical Methods for Agricultural Sciences”, Timber Press, USA , 225- (1998)
  • Ott, L., “An Introduction to Statistical Methods and Data Analysis, PWS Pub. Co, USA, 656-659 (1988) APPENDIX
  • A-) Problems used to estimate completed random block design parameters. Problem 1 (Artificial Data) Treatment 2 3 4 05 0.03 0.06 0.01 i 15 09 0 01 0.05 0 0.04 0.1 06 0.01 0.04 0 12 0.13 0.13 0.07 11 45 Y. j 0.06 065 07 26 07 0.075 0.07 0.065 0.28 067 0.072 0.069 0.060 0.268 197 0.212 0.204 0.195 0.808 j Problem 3 (Artificial Data) Treatment 2 3 4 i 21 19 20 78 17 19 19 71 23 20 24 86 61 58 63 235 j Problem 4 (Montgomery 1997) Treatment 2 3 4 4 i 3 9.3 6 4 9.3 9.8 9.9 38.4 2 9.4 9.5 9.7 37.8 6 2 5 6 37.7 38.9 39.8 154
  • Problem 5 (Artificial Data) Treatment 2 3 4 4 5 9.2 3 9.2 Y 9.2 3 4 5 37 5 8 37.2 37 37.1 148.1 j B-) Problems used to estimate balanced-incomplete random block design estimated parameters. Problem 1 (Artificial Data) Treatment 2 3 4 8 5 i 10.65 6 25 3 Y. j 5 25 3.55 5 3 8 55 10.55 11.3 11.4 Problem 2 (Artificial Data) Treatment 2 3 4 Y.ii 7.6 3 3 3.5 Y 6 2 4 8 5 10 4.4 4.8 29.7 7 j Problem 3 (Montgomery 1997) Treatment 2 3 4 75 68 - 72 75 222 224 207 218 i 218 214 Y. j
  • Problem 3 (Artificial Data) Treatment 2 3 4 4 5 9.2 3 6+y 9.2 Y 9.2 3 4 y 5 8 37.2 37 27.6+y 148.1 j 4 1 1 0 Y. j 5 4 4 8 2 1 y-2 -13 y-12 Problem 5 (Montgomery 1997) Treatment 2 3 4 1 2 1 5 2 Y 5 3 y 2 j
  • D-) Problems used to estimate random block design parameters in the case of two missing observations. Problem 1 (Montgomery 1997) Treat ment i 9.3 9.4 9.6 y 3 y1 + 9.4 9.3 9.8 9.9 9.2 9.4 9.5 9.7 9.7 9.6 10 y 4 8 Y. j 6 37.7 38.9 Block 2 3 4 Y.ii 0.05 0.03 0.06 0 0.04 0.03 0.01 y 01 0.15 02 0.09 0.04 0.05 y + y2 01 0.04 0 Y. j + 06 y2 08+ y1 13 0.07 0.34 y +
There are 18 citations in total.

Details

Primary Language English
Journal Section Statistics
Authors

Kamile Şanlı This is me

Ayşen Apaydın

Publication Date March 24, 2010
Published in Issue Year 2006 Volume: 19 Issue: 1

Cite

APA Şanlı, K., & Apaydın, A. (2010). Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review). Gazi University Journal of Science, 19(1), 41-48.
AMA Şanlı K, Apaydın A. Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review). Gazi University Journal of Science. March 2010;19(1):41-48.
Chicago Şanlı, Kamile, and Ayşen Apaydın. “Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review)”. Gazi University Journal of Science 19, no. 1 (March 2010): 41-48.
EndNote Şanlı K, Apaydın A (March 1, 2010) Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review). Gazi University Journal of Science 19 1 41–48.
IEEE K. Şanlı and A. Apaydın, “Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review)”, Gazi University Journal of Science, vol. 19, no. 1, pp. 41–48, 2010.
ISNAD Şanlı, Kamile - Apaydın, Ayşen. “Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review)”. Gazi University Journal of Science 19/1 (March 2010), 41-48.
JAMA Şanlı K, Apaydın A. Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review). Gazi University Journal of Science. 2010;19:41–48.
MLA Şanlı, Kamile and Ayşen Apaydın. “Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review)”. Gazi University Journal of Science, vol. 19, no. 1, 2010, pp. 41-48.
Vancouver Şanlı K, Apaydın A. Mathematical Programming for Estimation of Parameters in Random Blocks Model(Review). Gazi University Journal of Science. 2010;19(1):41-8.