Asymptotic expansions for modified maximum likelihood estimators with percentile truncated data
Saul Blumenthal · Communication in Statistics- Theory and Methods · 1985
Let be independent, identically distributed random variables with common distribution known except for the value of θ. Let be the order statistics, and assume that only the percentiles are observed where are given. Also, except for the assumption that N is also unknown. If N were known, this would represent type II censoring combined with a percentile equivalent of grouping. Estimators f o r both θ and N are found based on maximizing the weighted likelihood function (maximum likelihood being a special case ) . Asymptotic stochastic expansions for are developed for the case that (sampling is not truncated ) , and these are used to find expansions for when N is not known. Expansions for are developed from those for .The expansions include the second terms which lead t o the usual asymptotic normality results plus a third term which gives a second order bias correction.