Minimum variance unbiased estimation based on bootstrap iterations

Practical computation of the minimum variance unbiased estimator (MVUE) is often a difficult, if not impossible, task, even though general theory assures its existence under regularity conditions. We propose a new approach based on iterative bootstrap bias correction of the maximum likelihood estimator to accurately approximate the MVUE. Viewing bootstrap iteration as a Markov process, we develop a computational algorithm for bias correction based on arbitrarily many bootstrap iterations. The algorithm, when applied parametrically to finite sample spaces, does not involve Monte Carlo simulation. For infinite sample spaces, a nonparametric version of the algorithm is combined with a preliminary round of Monte Carlo simulation to yield an approximate MVUE. Both algorithms are computationally more efficient and stable than conventional simulation-based bootstrap iterations. Examples are given of both finite and infinite sample spaces to illustrate the effectiveness of our new approach. Supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7026/97P).