This paper deals with the task of parameter identification using the Bayes estimation method, which makes it possible to take into account the differing consequences of positive and negative estimation errors. The calculation procedures are based on the kernel estimators technique. The final result constitutes a complete algorithm usable for obtaining the value of the Bayes estimator on the basis of an experimentally obtained random sample. An elaborated method is provided for numerical computations.
Issue Section:
Technical Papers
1.
Lehmann, E. L., 1983, Theory of Point Estimation, Wiley, New York.
2.
Silverman, B. W., 1986, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
3.
Billingsley, P., 1979, Probability and Measure, Wiley, New York.
4.
Fisz, M., 1963, Probability Theory and Mathematical Statistics, Wiley, New York.
5.
Kulczycki
, P.
, 2000
, “Fuzzy Controller for Mechanical Systems
,” IEEE Trans. Fuzzy Syst.
, 8
, pp. 645
–652
.6.
Dertouzos, M. L., Athans, M., Spann, R. N., and Mason, S. J., 1972, Systems, Networks, and Computation: Basic Concepts, McGraw-Hill, New York.
7.
Kulczycki
, P.
, and Dawidowicz
, A. L.
, 1998
, “Kernel Estimator of Quantile
,” Universitatis Jagiellonicae Acta Mathematica
, 37
, pp. 101
–112
.8.
Parrish
, R. S.
, 1990
, “Comparison of Quantile Estimators in Normal Sampling
,” Biometrics
, 46
, pp. 247
–257
.9.
Kulczycki
, P.
, 1999a
, “A Random Approach to Time-Optimal Control
,” ASME J. Dyn. Syst., Meas., Control
, 121
, pp. 542
–543
.10.
Kulczycki
, P.
, 1999b
, “Random time-optimal control for mechanical systems
,” European Journal of Automation
, 33
, pp. 115
–140
.11.
Berger, J. O., 1980, Statistical Decision Theory, Springer-Verlag, New York.
Copyright © 2001
by ASME
You do not currently have access to this content.
