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We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors.
Fundamental limit theorems of probability theory
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The classical moment problem and some related questions in analysis
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On the closeness of the distributions of two sums of independent random variables
Zolotarev, V. M. (1965) · 1965
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On the accuracy of Gaussian approximation to the distribution functions of sums of independent variables
Ibragimov, I. A. (1966) · 1966
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An estimate of the remainder term in the multidimensional central limit theorem
Paulauskas, V. (1975) · 1975
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On the validity of the formal Edgeworth expansion
Bhattacharya, R. N. and Ghosh, J. K. (1978) · 1978
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Non-classical estimates of the rate of convergence in the multi-dimensional central limit theorem. I
Rotar’, V. (1978) · 1978
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Efron, B. (1979) · 1979
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On more precise convergence rate estimates in the central limit theorem
Ul’yanov, V. V. (1979) · 1979
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Probabilistic algorithms for sparse polynomials
Zippel, R. (1979) · 1979
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Fast probabilistic algorithms for verification of polynomial identities
Schwartz, J. T. (1980) · 1980
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On the asymptotic accuracy of Efron’s bootstrap
Singh, K. (1981) · 1981
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Bootstrapping regression models with many parameters
Bickel, P. J. and Freedman, D. A. (1983) · 1983
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Jackknife, bootstrap and other resampling methods in regression analysis
Wu, C. F. J. (1986) · 1986
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Moments and cumulants of the multivariate normal distribution
Holmquist, B. (1988) · 1988
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Bootstrap Procedures under some Non-I.I.D. Models
Liu, R. Y. (1988) · 1988
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Curto, R. E. and Fialkow, L. A. (1991) · 1991
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Hall, P. (1992) · 1992
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When does bootstrap work?
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Convex Optimization
Boyd, S. and Vandenberghe, L. (2004) · 2004
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Stein’s method for the bootstrap
Holmes, S. and Reinert, G. (2004) · 2004
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A Lyapunov-type bound in R d {R}^{d}
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Chatterjee, S. and Bose, A. (2005) · 2005
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An analogue of the Riesz–Haviland theorem for the truncated moment problem
Curto, R. E. and Fialkow, L. A. (2008) · 2008
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Some nonasymptotic results on resampling in high dimension. I. Confidence regions
Arlot, S., Blanchard, G., and Roquain, E. (2010) · 2010
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Efron, B. and Tibshirani, R. J. (1994) · 1994
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van der Vaart, A. W. and Wellner, J. A. (1996) · 1996
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