A New Approach of Point Estimation from Truncated or Grouped and Censored Data

TL;DR

This paper introduces a novel estimation method combining a new distance-based approach and traditional maximum likelihood estimation, specifically designed for truncated, grouped, and censored data, with proven convergence and practical applications.

Contribution

It presents a new estimation framework that integrates a minimum distance measure with classical methods, tailored for complex data censoring scenarios, and demonstrates its effectiveness and convergence.

Findings

Effective estimation on truncated and censored data.

Convergence in probability of the new estimator.

Potential for model selection and goodness-of-fit testing.

Abstract

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, the second based on maximum likelihood principle of known theoretical properties, and the first being as a control of the effectiveness of the obtained estimation, and for which we prove the convergence in probability, so we have also a criterion on the quality of the information contained in the observations. We apply the approach to truncated or grouped and censored 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.