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

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

Kamile Şanlı Ayşen Apaydın

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

Keywords

MINMAD, Goal Programming, Randomize Block Design, Completed Random Block

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• 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 +