The estimation of parameters from bulked samples

An estimation procedure has been developed for the estimation of parameters from bulked sample using the parametric bootstrap and density estimation in conjunction with the one-step maximum-likelihood estimator. It is shown that the proposed estimation procedure provides an asymptotically efficient estimator for parameters of interest when the density for the mean of the bulked samples has a certain form. The lognormal density (with sigma 2 assumed known) is an important distribution with the proper form. The finite sample performance for bulked samples based on underlying lognormal observations was examined by Monte Carlo study. The results indicate that the proposed procedure leads to a reduction in mean squared error compared to known procedures.