Homogeneity tests for interval data

Abstract

In many practical situations, we only know the upper bound ∆ of the measurement error. It means that the precise measurement is located on the interval (x – ∆, x + ∆). In other words, the data can be represented as a sample of interval observations. When performing statistical tests, ignoring this uncertainty in data may lead to unreliable decisions. For interval data, standard nonparametric and semiparametric methodologies include various modifications of the logrank test for comparing distribution functions. The statistics of the logrank homogeneity tests are based on comparing the nonparametric maximum likelihood estimates (NPMLE) of the distribution functions. In this paper, NPMLE is calculated by the ICM-algorithm (iterative convex minorant algorithm). The purpose of this paper is to investigate some homogeneity tests for interval data and to carry out the comparative analysis in terms of the power of tests for close competing hypotheses.