Gaussian approximation of suprema of empirical processes

Kolmogorov, A. (1933). Sulla determinazione empirica di una legge di distribuzione

1933

Earlier work this paper cites.

Stein, C. (1972). A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In:

1972

Earlier work this paper cites.

Bickel, P.J. and Rosenblatt, M. (1973). On some global measures of the deviations of density function estimates

1973

Earlier work this paper cites.

Komlós, J., Major, P., and Tusnády, G. (1975). An approximation for partial sums of independent rv’s and the sample df I

1975

Earlier work this paper cites.

Yurinskii, V.V. (1977). On the error of the Gaussian approximation for convolutions

1977

Earlier work this paper cites.

Koenker, R. and Bassett G.W. (1978). Regression quantiles

1978

Earlier work this paper cites.

Dehling, H. (1983). Limit theorems for sums of weakly dependent Banach space valued random variables

1983

Earlier work this paper cites.

Dudley, R.M. and Philipp, W. (1983). Invariance principles for sums of Banach space valued random elements and empirical processes

1983

Earlier work this paper cites.

Konakov, V.D. and Piterbarg, V.I. (1984). On the convergence rate of maximal deviations distributions for kernel regression estimates

1984

Earlier work this paper cites.

Stein, C. (1986)

1986

Earlier work this paper cites.

Mason, D.M. and van Zwet, W.R. (1987). A refinement of the KMT inequality for the uniform empirical process

1987

Earlier work this paper cites.

Nolan, D. and Pollard, D. (1987)

1987

Earlier work this paper cites.

Zaitsev, Y. (1987). On the Gaussian approximation of convolutions under multidimensional analogues of S.N. Bernstein’s inequality conditions

Original

1987

Earlier work this paper cites.

Le Cam, L. (1988). On the Prokhorov distance between the empirical process and the associated Gaussian bridge. Technical Report No. 170, Department of Statistics, University of California, Berkeley

1988

Earlier work this paper cites.

Bretagnolle, J. and Massart, P. (1989). Hungarian construction from the non asymptotic viewpoint

1989

Earlier work this paper cites.

Massart, P. (1989). Strong approximation for multivariate empirical and related processes, via KMT construction

1989

Earlier work this paper cites.

Ledoux, M. and Talagrand, M. (1991)

1991

Earlier work this paper cites.

Norvaiša, R. and Paulauskas, V. (1991). Rate of convergence in the Central Limit Theorem for empirical processes

1991

Earlier work this paper cites.

Cohen, A., Daubechies, I., and Vial, P. (1993). Wavelets on the interval and fast wavelet transforms

1993

Earlier work this paper cites.

Csörgo, M. and Horváth, L. (1993)

1993

Earlier work this paper cites.

Montgomery-Smith, S. (1993). Comparison of sums of independent identically distributed random vectors

1993

Earlier work this paper cites.

Deheuvels, P. and Mason, D.M. (1994). Functional laws of the iterated logarithm for local empirical processes indexed by sets

1994

Earlier work this paper cites.

Koltchinskii, V.I. (1994). Komlós-Major-Tusnády approximation for the general empirical process and Haar expansions of classes of functions

1994

Cited alongside, same era.

Rio, E. (1994). Local invariance principles and their application to density estimation

1994

Cited alongside, same era.

Talagrand, M. (1996). New concentration inequalities in product spaces

1996

Cited alongside, same era.

van der Vaart, A.W. and Wellner, J.A. (1996)

1996

Cited alongside, same era.

Einmahl, U. and Mason, D.M. (1997). Gaussian approximation of local empirical processes indexed by functions

1997

Cited alongside, same era.

Newey, W.K. (1997). Convergence rates and asymptotic normality for series estimators

1997

Talagrand, M. (2005)

2005

Later among the works it cites.

Berthet, P. and Mason, D.M. (2006). Revisiting two strong approximation results of Dudley and Philipp. In:

2006

Later among the works it cites.

Chatterjee, S. and Meckes, E. (2008). Multivariate normal approximation using exchangeable pairs

2008

Later among the works it cites.

Giné, E. and Nickl, R. (2009). Uniform limit theorems for wavelet density estimators

2009

Later among the works it cites.

Meckes, E. (2009). On Stein’s method for multivariate normal approximation. In:

2009

Later among the works it cites.

Reinert, G. and Röllin, A. (2009). Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition

2009