Maximum entropy principle and statistical inference on condensed ordered data

Using sample quantiles, a point estimation procedure based on the maximum entropy principle is proposed. Under standard regularity conditions it is shown that these estimators are efficient and asymptotically normal. A goodness-of-fit test statistic is also given and its asymptotic chi-square distribution is calculated. The testing mechanism has the advantage with respect to the usual chi-square goodness-of-fit test that it is possible to avoid the difficulties of choosing cell boundaries for grouping.