Unbiased Estimation for a Multivariate Exponential whose Components have a Common Shift

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It is shown that for independent and identically distributed random vectors, for which the components are independent and exponentially distributed with a common shift, we can construct unbiased estimators of their density, derived from the Uniform Minimum Variance Unbiased Estimator (UMVUE) of their distribution function. As direct applications of the UMVUEs of the density functions we present a Chi-square goodness of fit test of the model, and give two tables of the UMVUEs of some commonly used functions of the unknown parameters of the multivariate exponential model considered in this paper.