Testing hypotheses in truncated samples by means of divergence statistics

In this paper we consider the problem of testing hypotheses in parametric models, when only the first gamma (of n) ordered observations are known. Using divergence measures,a procedure to test statistical hypotheses is proposed. Replacing the parameters by suitable estimators in the expresion of the divergence measure, the test statistics are obtained. Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators for truncated samples are considered. Applications of these results in testing statistical hypotheses, on the basis of truncated data, are presented. The small sample behavior of the proposed test statistics is analyzed in particular cases. A comparative study of power values is carried out by computer simulation.