Nonparametric scale tests based on the notion of data depth

Percentile modification concerns with using only fraction of the sample observations in computation of the test statistic. The modification improves power of rank based tests given appropriate amount of percentile modification is performed. This paper addresses the problem of deciding amount of percentile modification in context of two sample, multivariate scale problem using data depth. We propose an adaptive test which decides amount of modification based on tail heaviness of the data. As a second approach, we define three test statistics on a group of percentile modified statistics using different combining functions, viz. a quadratic form, a maximum-type and a sum-type. With this strategy, the task of choosing a single optimum value as an amount of percentile modification becomes irrelevant. Monte-Carlo simulation is used to perform comparative power study. Adaptive test as well as sum-type and maximum-type statistics based on a group of percentile modified statistics yield attractive powers whereas quadratic form statistics do not show promising results.