A note on estimation based on record data

In data-processing standpoint, an efficient algorithm for identifying the minimum value among a set of measurements are record statistics. From a sequence of n independent identically distributed continuous random variables only about log(n) records are expected, so we expect to have little data, hence any prior information is welcome (Houchens, Record value theory and inference, Ph.D. thesis, University of California, Riverside, 1984). In this paper, non-Bayesian and Bayesian estimates are derived for the two parameters of the Exponential distribution based on record statistics with respect to the squared error and Linear-Exponential loss functions and then compared with together. The admissibility of some estimators is discussed.