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Abstract:
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Suppose $(X,Y)$ has a Downton's bivariate exponential distribution with correlation $\rho$. For a random sample of size $n$ from $(X,Y)$, let X_{r:n}$ be the $r$th $X$-order statistic and $Y_{[r:n]}$ be its concomitant. We investigate estimators of $\rho$ when all the parameters are unknown and the available data is an incomplete bivariate sample made up of (i) all the $Y$ values and the ranks of associated $X$ values, i.e., $(i, Y_{[i:n]}), 1 \leq i \leq n$, and (ii) a Type II censored bivariate sample consisting of $(X_{i:n}, Y_{[i:n]}), 1 \leq i \leq r < n$. In both setups, we use simulation to examine the bias and mean square errors of several estimators of $\rho$ and obtain their estimated relative efficiencies.
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