On Estimation of the Correlation Coefficient and
Testing of Independence in the Moran-Downtown Bivariate and Multivariate
Exponential Distributions.
ABSTRACT:
In this talk, I will discuss some estimators for the correlation
coefficient $\rho$ in Moran-Downton bivariate exponential distribution and
introduce two simple bias-reduced estimators. I will also discuss the use
of jackknife method in order to reduce the bias of all these
estimators. Using Monte Carlo simulations, I will then compare the
performance of all these estimators.
Next, I will generalize the proposed estimators to pooled estimators for
the correlation coefficient $\rho$ in equicorrelated multivariate
exponential distribution. I will also discuss the maximum likelihood
estimators and their asymptotic properties. Once again, using Monte Carlo
simulations, I will compare the performance of these estimators.
Finally, I will propose some test statistic (based on these
estimators) for testing the total independence of bivariate and
multivariate exponential variables. A comparison of the power performance
of these tests will be briefly made.
About the Speaker
H. K. T. Ng is a Ph.D. candidate in statistics at McMaster
University, Hamilton, Canada. He received the B.Sc.(Hon.) (1997) and
M.Phil. (1999) in statistics from the Chinese University of Hong Kong, and
the M.Sc. (2000) in statistics from McMaster University, Canada. His
research interests include order statistics, reliability theory and
analysis of censored data.
References
The following are background references and the paper on which the talk
is based. All references are available at the Thode library.
Al-Saadi, S. D., Scrimshaw, D. F. and Young, D. H. (1979) Tests for
independence of exponential variables, Journal of Statistical
Computation and Simulation, 9, 217-233.
Al-Saadi, S. D. and Young, D. H. (1980) Estimators for the
correlation coefficient in a bivariate exponential distribution,
Journal of Statistical Computation and Simulation, 11, 13-20.
Al-Saadi, S. D. and Young, D. H. (1982) A test for independence in a
multivariate exponential distribution with equal correlation coefficient,
Journal of Statistical Computation and Simulation, 14.
219-227.
Balakrishnan, N. and Ng, H. K. T. (2001) Improved estimation of the
correlation coefficient in a bivariate exponential distribution,
Journal of Statistical Computation and Simulation, 68,
173-184.
