Here is the part of the definition I don't get: Given $X^n$, let $\hat{F}$ be a CDF that is absolutely continuous on $F_e \ \ (\hat{F}\ll F_e)$. What does it mean?
2026-02-24 09:54:21.1771926861
If $\hat{F}$ - estimated empirical CDF, then what does $(\hat{F}) \ll F_{empirical}$ mean? (Absolutely continuous on $F_{emp}$)
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Consider a probability measure $\hat{\mu}_n$ with distribution function $\hat{F}$ and a probability measure $\mu_e$ with distribution function $F_e$. Then $\hat{\mu}_n$ should be absolutely continious with respect to measure $\mu_e$.