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Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis
American Journal of Theoretical and Applied Statistics
Volume 2, Issue 5, September 2013, Pages: 142-148
Received: Aug. 6, 2013; Published: Sep. 10, 2013
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Apantaku Fadeke Sola., Department of Statistics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
Olayiwola Olaniyi Mathew, Department of Statistics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
Adewara Amos Adedayo, Department of Statistics, University of Ilorin, Nigeria
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The problem of allocation with more than one characteristic in stratified sampling is conflicting in nature, as the best allocation for one characteristic will not in general be best for others. Some compromise must be reached to obtain an allocation that is efficient for all characteristics. In this study, the allocation of a sample to strata which minimizes cost of investigation, subject to a given condition about the sampling error was considered. The data on four socioeconomic characteristics of 400 heads of households in Abeokuta South and Ijebu North Local Government Areas (LGAs) of Ogun State, Nigeria were investigated. These comprised of 200 households from each LGA. The characteristics were occupation, income, household size and educational level. Optimal allocation in multi-item was developed as a multivariate optimization problem by finding the principal components. This was done by determining the overall linear combinations that concentrates the variability into few variables. From the principal component analysis, it was seen that for both Abeokuta and Ijebu data sets, the variance based on the four characteristics as multivariate is less than that of the variables when considered as a univariate. From the results, it was seen that there was no difference in the percentage of the total variance accounted for by the different components from the merged sample when compared with the individual sample. Optimum allocation was achieved when there was stratification
Stratified Sampling, Optimum Allocation, Stratification, Optimization
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Apantaku Fadeke Sola., Olayiwola Olaniyi Mathew, Adewara Amos Adedayo, Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis, American Journal of Theoretical and Applied Statistics. Vol. 2, No. 5, 2013, pp. 142-148. doi: 10.11648/j.ajtas.20130205.14
Bankier, M. D. 1996. Estimators based on several stratified samples with applications to multiple frame survey. Journal of American Stat. Assoc. 81: 1074 – 1079.
Cheang, C. 2011. Sampling strategies and their advantages and disadvantages. (Accessed March 5, 2011).
Cochran, W. G. 1977. Sampling Techniques (3rd Edition), New York, Wiley.
Diaz-Garcia, J.A and Ramos-Quiroga, R. 2011. Multivariate Stratified Sampling by Stochastic Multi Objective Optimization. Xiv: 1106.0773VI. Statistical Methodology. XIV, 1116-1123.
Diaz-Garcia, J. A. and Cortez, L. U. 2006. Optimum allocation in multivariate stratified sampling: multi-objective programming. Communicacion Technica: Communicaciones Del CIMAT. 6(7), 28-33.
Hartley, H. O. 1962. Multiple frame surveys: Proceeding of the social statistics section of American Statistical Association, 205 – 215.
Hartley, H. O. 1964. A new estimation theory for sampling surveys. Biometrics, 55, 545 – 557.
Khan, M.G.M and Ahsan, M.J. 2003. A note on Optimum Allocation in Multivariate Stratified Sampling. South Pacific Journal Natural Science, 21, 91-95.
Kokan, A.R and Khan, S.U., 1967. Optimum allocation in mutivariate surveys. An analytical solution. Journal of Royal Statistical Society. Series B, 29, 115-125.
Lumley, T. 2004. Analysis of complex survey samples. Department of Biostatistics. University of Washington Press.
Miettinen, K. M. 1999. Non linear multi-objective optimization. Kluwer Academic Publishers, Boston.
Pirzada, S. and Maqbool, S. 2003. Optimal Allocation in Multivariate sampling Through Chebyshev’s Approximation. Bulletin of the Malaysian Mathematical Science Society, 2, (26), 221 – 230.
Saxens, J., Narain, M. U. and Srivastava, S. 1986. The maximum likelihood method for non-response in Surveys. Survey Methodology. 12, 50 – 62.
Sethna, B. N. and Groeneveld, L. 1984. Research Methods in Marketing and Management. Tata, Mcgraw-Hill, publishing, New-Delhi.
Steuer, R.E. 1986. Multiple criteria optimization: Theory, Computation and applications. John Wiley, New York.
Winship, C. and Radbill, L. 1994. Sampling weights and regression analysis. Sociological Methods and Research, 23, (2), 230 – 257.
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