Abstract
In this dissertation a family of procedure for the simultaneous estimation of parameters is developed. The procedures are applicable to location/scale families of distribution, as well as to many other interesting families, including those with differing types of truncation as well as the three-parameter Weibull and lognormal distribution. They are based upon the empirical quantile function and fall into the general class of minimum distance estimators. The estimator is taken as that vector of parameters which minimizes a "distance" measure between the empirical quantile function and a parametric family of population quantile function. These estimators can be considered as generalization of the procedures developed by Lloyd (1952), Blom (1958) and Parzen (1979). Under suitable regularity conditions the estimators are shown to be consistent and to have asymptotically a multivariate normal distribution. The influence curves are determined, and the estimators are shown to be robust. Two specific forms of the procedure are shown to be regular best asymptotic normal estimators. Finally, a goodness-of-fit test statistic based upon the technique is given. The procedures are then applied to some published data sets.
LaRiccia, V. N. (1979). A family of minimum quantile distance estimators. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -661601.