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On Convergence of Stratification Algorithms for Skewed Populations
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 Title & Authors
On Convergence of Stratification Algorithms for Skewed Populations
Park, In-Ho;
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For stratifying skewed populations, the Lavalle-Hidiroglou(LH) algorithm is often considered to have a take-all stratum with the largest units and some take-some strata with the middle-size and small units. Related to its iterative nature have been reported some numerical difficulties such as the dependency of the ultimate stratum boundaries to a choice of initial boundaries and the slow convergence to locally-optimum boundaries. The geometric stratification has been recently proposed to provide initial boundaries that can avoid such numerical difficulties in implementing the LH algorithm. Since the geometric stratification does not pursuit the optimization but the equalization of the stratum CVs, the corresponding stratum boundaries may not be (near) optimal. This paper revisits these issues concerning convergence and near-optimality of optimal stratification algorithms using artificial numerical examples. We also discuss the formation of the strata and the sample allocation under the optimization process and some aspects related to discontinuity arisen from the finiteness of both population and sample as well.
Lavalle-Hidiroglou(LH) algorithm;geometric stratification;random search algorithm;stratum boundaries;optimization;
 Cited by
Cochran, W. G. (1961). Comparison of methods for determining stratum boundaries, Bulletin of the International Statistical Institute, 32, 345–358

Gunning, P. and Horgan, J. M. (2004). A new algorithm for the construction of stratum boundaries in skewed populations, Survey Methodology, 30, 159–166

Gunning, P., Horgan, J. M. and Keogh, G. (2008). An implementation strategy for efficient convergence of the Lavall´ee and Hidiroglou stratification algorithm, Journal of Official Statistics, 24, 213–228

Horgan, J. M. (2006). Stratification of skewed populations, International Statistical Review, 74, 67–76

Kozak, M. (2004). Optimal stratification using random search method in agricultural surveys, Statistics in Transition, 6, 797–806

Kozak, M. and Verma, M. R. (2006). Geometric versus optimization approach to stratification: A comparison of efficiency, Survey Methodology, 32, 157–163

Lavallee, P. and Hidiroglou, M. (1988). On the stratification of skewed populations, Survey Methodology, 14, 33–43

Rivest, L. -P. (2002). A generalization of Lavallee and Hidiroglou algorithm for stratifications in business survey, Survey Methodology, 28, 191–198

Sigman, R. and Monsour, N. (1995). Selecting samples from list frame of business, In Business Survey Methods, John Wiley & Sons, New York

Slanta, J. and Krenzke, T. (1996). Applying the Lavallee and Hidiroglou method to obtain stratification boundaries for the Census Bureau's Annual Capital Expenditure Survey, Survey Methodology, 22, 65–75