Recently, I'm studying Nonparametric methods, especially Order Statistics.
And I saw a sentence which says that Order statistic has to be evenly selected.
And now I'm wondering what 'evenly selected' means
and I want to know if there's a method of testing evenness of selected order statistic or not.
Thanks for your help!
Remember that the order statistics represent percentile estimates (specifically, $\frac{1}{N}$ percentiles) of some unknown distribution. In nonparametric statistics, you are basically working with the empirical CDF, which places $\frac{1}{N}$ probability on each data point, hence on each order statistic. I think your text is referring to the idea that there cannot be preferential sampling of the sample space, i.e., sampling with a uniform probability of each sample point. If there is preferential sampling (i.e., importance sampling), then you are in the realm of parametric statistics.
You can't test this as it's an assumption and should be baked into your sampling plan.