Estimation of Location Parameter from Two Biased Samples

DOI: 10.4236/am.2013.49171   PDF   HTML     3,710 Downloads   5,005 Views  

Abstract

We consider a problem of estimating an unknown location parameter from two biased samples. The biases and scale parameters of the samples are not known as well. A class of non-linear estimators is suggested and studied based on the fuzzy set ideas. The new estimators are compared to the traditional statistical estimators by analyzing the asymptotical bias and carrying out Monte Carlo simulations.

Share and Cite:

L. Piterbarg, "Estimation of Location Parameter from Two Biased Samples," Applied Mathematics, Vol. 4 No. 9, 2013, pp. 1269-1277. doi: 10.4236/am.2013.49171.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] G. Casella and R. Berger, “Statistical Inference,” 2nd Edition, Brooks/Cole, Pacific Grove, 1990.
[2] M. Ghil, “Meteorological Data Assimilation for Oceanographers. Part 1; Description and Theoretical Framework,” Dynamics of Atmospheres and Oceans, Vol. 13, No. 2, 1989, pp. 171-218.
doi:10.1016/0377-0265(89)90040-7
[3] P. Malanotte-Rizzoli, “Modern Approaches to Data Assimilation in Ocean Modeling,” Elsevier, Amsterdam, 1996.
[4] T. Krishnamurti, C. Kishtawal, Z. Zhang, T. Larow, D. Bachiochi and E. Williford, “Multimodel Ensemble Forecasts for Weather and Seasonal Climate,” Journal of Climate, Vol. 13, No. 8, 2000, pp. 4196-4216. doi:10.1175/1520-0442(2000)013<4196:MEFFWA>2.0.CO;2
[5] F. J. Lenartz, M. Beckers, J. Chiggiato, B. Mourre, C. Troupin, L. Vandenbulcke and M. Rixen, “Super Ensem ble Techniques Applied to Wave Forecast: Performance and Limitations,” Ocean Science, Vol. 6, No. 3, 2010, pp. 595-604. doi:10.5194/os-6-595-2010
[6] D. Dubois and H. Prade, “Possibilty Theory,” Plenum Press, New York, London, 1988. doi:10.1007/978-1-4684-5287-7
[7] G. Shafer, “A Mathematical Theory of Evidence,” Princeton University Press, Hoboken, 1976.
[8] T. P. Hill and J. Miller, “How to Combine Independent Data Sets for the Same Quantity,” Chaos, Vol. 21, No. 3, 2011, p. 3. doi:10.1063/1.3593373
[9] L. I. Piterbarg, “Parameter Estimation from Small Biased Samples: Statistics vs Fuzzy Logic,” Fuzzy Sets and Sys tems, Vol. 170, No. 1, 2011, pp. 1-21. doi:10.1016/j.fss.2011.01.010
[10] K. Deb, “Multi-Objective Optimization Using Evolution ary Algorithms,” Willey, Princeton, 2001.
[11] R. J. Huber, “Robust Estimation of a Location Parame ter,” The Annals of Mathematical Statistics, Vol. 35, No. 1, 1964, pp. 73-101. doi:10.1214/aoms/1177703732

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.