We derive limit theorems for the empirical distribution function of "devolatilized" increments of an Ito semimartingale observed at high frequencies. These "devolatilized" increments are formed by ...

The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincaré-type or logarithmic Sobolev inequalities. The general concentration results are then ...

The empirical distribution function of a sample, F n (y), is the proportion of observations less than or equal to y. where n is the number of observations, and is an indicator function with value 1 if ...

When you use a WEIGHT statement, the percentiles are computed differently. The 100pth weighted percentile y is computed from the empirical distribution function with averaging where w i is the weight ...