Interval statistics: Maximum likelihood method and method of moments (Q1269937)

In the interval mathematical statistics of interval data (for brevity we shall speak of interval statistics), it is assumed that the observations are represented by intervals. In traditional statistics they are characterized by numbers. Using intervals, we can study the influence of errors on the properties of statistical procedures. Therefore, in some papers the term ``realistic statistics'' was used. It became clear after the International Conference on Interval and Stochastic Methods in Science and Technology INTERVAL-92 that Russian researchers are at the forefront of the development of interval statistics. The present paper extends the investigations begun by the author in 1988. In classical mathematical statistics, it was shown that in estimation theory the maximum likelihood method is usually better (in the sense of the asymptotic variance) than the method of moments. However, this is not so in interval statistics, where the estimation of the parameters of the gamma-distribution was considered. The aim of this paper is to study these two estimation methods in the case of interval data. Since the maximum likelihood method is a special case of the minimum contrast method, we begin this paper with a description of this method.