Correlation estimation in Downton's bivariate exponential distribution using incomplete samples

Abstract

Suppose (X, Y) has a Downton's bivariate exponential distribution with correlation ρ. For a random sample of size n from (X, Y), let X _r:n be the rth X-order statistic and Y _[r:n] be its concomitant. We investigate estimators of ρ 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≤i≤n, and (ii) a Type II right-censored bivariate sample consisting of (X _i:n , Y _[i:n]), 1≤i≤r<n. In both setups, we use simulation to examine the bias and mean square errors of several estimators of ρ and obtain their estimated relative efficiencies. The preferred estimator under (i) is a function of the sample correlation of (Y _i:n , Y _[i:n]) values, and under (ii), a method of moments estimator involving the regression function is preferred.

Keywords:

• concomitants of order statistics
• Type II censoring
• correlation coefficient
• estimation
• simulation
• relative efficiency

AMS Subject Classification :

• 62N02
• 62G30
• 62G05