The following comments are focus setting: The correlation ratio is frequently used as a measure of the performance of the best predictor (in the least square sense) of an order statistic as a function of all other order statistics from the same sample.Prior research focused on upper bounds for coefficient of determination between two order statistics, assuming the original observations are and. The present paper focuses on the case when the observations are identically distributed but not independent. Specifically, the order statistics are obtained in a sample without replacement from a finite population. Sampling without replacement is the most natural method in practical applications and hence its background focus here. Under this setting, the paper presents lower and upper bounds for the correlation ratio between any two order statistics.
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