A New Approach of Point Estimation and its Application to Truncated Data Situations
Résumé
We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between variations of two distributions on a finite number of points from their support and on using this measure for estimation purposes by the method of minimum distance. For the second method, given an empirical discrete distribution, we build up an auxiliary discrete theoretical distribution having the same support of the first and depending on the same parameters of the parent distribution of the data from which the empirical distribution emanated. We estimate then the parameters from the empirical distribution by the usual statistical methods. In practice, we propose to compute the two estimations and we choose the second, of known theoretical properties, and let the first being as a control of the effectiveness of the obtained estimation, so we have also a criterion on the quality of the information contained in the observations. We apply the approach to truncated data situations to give the flavour on the effectiveness of the approach. We give also some interesting perspectives of the approach including model selection from truncated data, estimation of the initial trial value in the celebrate EM algorithm in the case of truncation and merged normal populations, a test of goodness of fit based on the new distance, quality of estimations and data, optimum number of classes in grouping data from continuous distributions.
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