On adjusted method of moments estimators on uniform distribution samples

In this article, we prove that with probability one the k-th order upper random Stieltjes sum defined on a random sample from a distribution supported by a finite interval converges to the corresponding k-th moment distribution. When the underlying distribution is uniform U(0,θ), we prove that the adjusted method of moments (AMM) estimator, introduced by Soltani and Homei (2009a), is indeed strongly consistent and asymptotically unbiased for the parameter 9. We demonstrate that the asymptotic distribution of the AMM estimator is not normal, and introduce a pivotal variable for inference on θ using the AMM estimator. The upshot is that the mean square relative error for θ<Superscript>2</Superscript> using the square AMM estimator is asymptotically 1/2 of the corresponding term using the MLE. Copyright Sapienza Università di Roma 2012