Efficiency of the Estimators of Multivariate Distribution Parameters from the One-Dimensional Observed Frequencies.

摘要

Parameter estimation for multivariate probability distributions is studied in experiments where data are presented as one-dimensional histograms. For this model a statistic defined as a quadratic form of the observed frequencies which has a limiting x/sup 2/-distribution is proposed. The efficiency of the estimator minimizing the value of that statistic is proved whithin the class of all unbiased estimates obtained via minimization of quadratic forms of observed frequencies. The method was applied to the physical problem of analysis of the secondary pion energy distribution in the isobar model of pion-nucleon interactions with the production of an additional pion. The numerical experiments showed that the accuracy of estimation is twice as much if comparing the conventional methods. 3 refs.; 1 fig. (Atomindex citation 20:030751)