Abstract
We consider the optimal design problem when the design space consists of binary vectors with a string property, i.e., a single stretch of ones. This is done in the framework of second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. Analytical as well as computational results on optimal design measures, under the D- and A-criteria, are obtained. The issue of robustness to the unknown skewness parameter of the error distribution is also explored. Finally, we present several procedures which entail N-run designs that are highly efficient, if not optimal.
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References
Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Stat 12:171–178
Bose M, Mukerjee R (2015) Optimal design measures under asymmetric errors, with application to binary design points. J Stat Plan Inf 159:28–36
Gao LL, Zhou J (2014) New optimal design criteria for regression models with asymmetric errors. J Stat Plan Inf 149:140–151
Gao LL, Zhou J (2016) D-optimal designs based on the second-order least squares estimator. Stat Pap. doi:10.1007/s00362-015-0688-9
Huda S, Khan IH, Mukerjee R (1995) On optimal designs with restricted circular string property. Comput Stat Data Anal 19:75–83
Jacroux M (1986) On the E- and MV-optimality of spring balance designs with string property. J Stat Plan Inf 13:89–96
Mukerjee R, Huda S (2016) Approximate theory-aided robust efficient factorial fractions under baseline parametrization. Ann Inst Stat Math. doi:10.1007/s10463-015-0509-x
Mukerjee R, Saharay R (1985) Asymptotically optimal weighing designs with string property. J Stat Plan Inf 12:87–91
Schiffl K, Hilgers DT (2012) A-optimal designs for two-color microarray experiments for treatment-control and all-to-next contrasts. Commun Stat Simul Comput 41:1142–1151
Sinha BK, Saha R (1983) Optimal weighing designs with a string property. J Stat Plan Inf 8:365–374
Wang L, Leblanc A (2008) Second-order nonlinear least squares estimation. Ann Inst Stat Math 60:883–900
Acknowledgments
Thanks are due to the referees for very constructive suggestions. The work of RM was supported by a grant from the Indian Institute of Management Calcutta and the J.C. Bose National Fellowship of the Government of India.
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Huda, S., Mukerjee, R. Optimal designs with string property under asymmetric errors and SLS estimation. Stat Papers 59, 1255–1268 (2018). https://doi.org/10.1007/s00362-016-0819-y
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DOI: https://doi.org/10.1007/s00362-016-0819-y