Weak Convergence of Smoothed Empirical Processes
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Let XI, X2, . . . be a sequence of i.i.d. random variables with common law P. The nth empirical measure is PD. = n - S1 bx= and its smoothed version is DPn, = 9n * P)n for a sequence of random signed measures an converging weakly in probability to zero. We give conditions for the weak convergence of the smoothed empirical processes ln(Pnf - P).
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