Estimation of parametric functions in
Downton's bivariate exponential distribution
George Iliopoulos
This paper considers estimation of the ratio of means and the regression
function in Downton's (1970) bivariate exponential distribution. Unbiased estimators
are given and, by presenting improved estimators, they are shown to be
inadmissible in terms of mean squared error. The results are derived by
conditioning on an unobserved random sample from a geometric distribution which
provides conditional independence for the statistics involved.
AMS 2000 subject classifications: 62F10, 62C99.
Key words and phrases: Downton's bivariate exponential distribution,
unbiased estimation, ratio of means, regression function, mean squared error,
inadmissibility.