Multi-Aspect Tests with Sample Quantiles

In this research, we consider multi-aspect tests based on the quantile statistics. The multi-aspect tests would be efficient in terms of power when the underlying distributions may not be known or quite different types. First of all, we use the quadratic form for the test statistic to combine several quantile statistics, which would be suitable for the general type of alternative. Also we consider sum type of statistic for the quantile functions which may be applied for the one-sided alternative. We derive the asymptotic normalities for both cases applying the large sample approximation theorem. Further, we apply the permutation principle with the Monte-Carlo method to obtain the exact null distributions and state briefly the order of application of the permutation principle. Then we illustrate our procedure with a numerical example by obtaining p-values using both methods. Finally we discuss the combination functions and resampling methods as concluding remarks.