Central limit theorem for integrated square error of multivariate nonparametric density estimators
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Bickel, 1973, On some global measures of the deviations of density function estimates, Ann. Statist., 1, 1071, 10.1214/aos/1176342558
Bowman, 1982, A comparative study of some kernel-based nonparametric density estimates, Manchester-Sheffield School of Probability and Statistics Research Report 84/AWB/1
Brown, 1971, Martingale central limit theorems, Ann. Math. Statist., 42, 59, 10.1214/aoms/1177693494
Cs̈orgö, 1981
Gregory, 1977, Large sample theory for U-statistics and tests of fit, Ann. Statist., 5, 110, 10.1214/aos/1176343744
Hall, 1979, On the invariance principle for U-statistics, Stochastic Process. Appl., 9, 163, 10.1016/0304-4149(79)90028-0
Hall, 1982, Limit theorems for stochastic measures of the accuracy of density estimators, Stochastic Process. Appl., 13, 11, 10.1016/0304-4149(82)90003-5
Hall, 1982, Large sample optimality of least squares cross-validation in density estimation, Ann. Statist.
Hall, 1980
Komlós, 1975, An approximation of partial sums of independent r.v.'s and the sample d.f. I, Z. Wahrsch. Verw. Gebiete, 32, 111, 10.1007/BF00533093
Mack, 1979, Multivariate k-nearest neighbour density estimates, J. Multivar. Anal., 9, 1, 10.1016/0047-259X(79)90065-4
Neuhaus, 1977, Functional limit theorems for U-statistics in the degenerate case, J. Multivar. Anal., 7, 424, 10.1016/0047-259X(77)90083-5
Rosenblatt, 1975, A quadratic measure of deviation of two-dimensional density estimates and a test of independence, Ann. Statist., 3, 1, 10.1214/aos/1176342996
Weber, 1981, Incomplete degenerate U-statistics, Scand. J. Statist., 8, 120