论文信息 - Weak Convergence of Smoothed Empirical Processes

Weak Convergence of Smoothed Empirical Processes

Let (Xi)i_1 be a sequence of i.i.d. random variables with common law P on RI, d ) 1. The nth empirical measure is P. = n - 1= 1 kx and its smoothed version is P. = On*P. where (Pn)i is a sequence of probability measures converging weakly to &0. We find sufficient conditions implying

Joseph E. Yukich | J. Yukich

[1] B. B. Winter. Strong uniform consistency of integrals of density estimators , 1973 .

[2] J. Yukich. A note on limit theorems for perturbed empirical processes , 1989 .

[3] Hajime Yamato,et al. UNIFORM CONVERGENCE OF AN ESTIMATOR OF A DISTRIBUTION FUNCTION , 1973 .

[4] B. K. Ghosh,et al. The Power and Optimal Kernel of the Bickel-Rosenblatt Test for Goodness of Fit , 1991 .

[5] E. Giné,et al. Some Limit Theorems for Empirical Processes , 1984 .

[6] R. Dudley. An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions , 1985 .

[7] L. Fernholz,et al. Almost sure convergence of smoothed empirical distribution functions , 1991 .

[8] D. Pollard. Convergence of stochastic processes , 1984 .

[9] R. Dudley. A course on empirical processes , 1984 .