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Relevant bibliographies by topics / Berry-Esséen theorem

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Academic literature on the topic 'Berry-Esséen theorem'

Author: Grafiati

Published: 24 April 2022

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Journal articles on the topic "Berry-Esséen theorem"

1

Hallin, Marc, and Khalid Rifi. "A Berry-Esséen Theorem for Serial Rank Statistics." Annals of the Institute of Statistical Mathematics 49, no. 4 (1997): 777–99. http://dx.doi.org/10.1023/a:1003286814679.

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2

Quine, M. P., and J. S. Law. "Modelling random linear nucleation and growth by a Markov chain." Journal of Applied Probability 36, no. 01 (1999): 273–78. http://dx.doi.org/10.1017/s0021900200017034.

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In an attempt to investigate the adequacy of the normal approximation for the number of nuclei in certain growth/coverage models, we consider a Markov chain which has properties in common with related continuous-time Markov processes (as well as being of interest in its own right). We establish that the rate of convergence to normality for the number of ‘drops’ during times 1,2,…n is of the optimal ‘Berry–Esséen’ form, as n → ∞. We also establish a law of the iterated logarithm and a functional central limit theorem.

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3

Quine, M. P., and J. S. Law. "Modelling random linear nucleation and growth by a Markov chain." Journal of Applied Probability 36, no. 1 (1999): 273–78. http://dx.doi.org/10.1239/jap/1032374248.

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Abstract:

In an attempt to investigate the adequacy of the normal approximation for the number of nuclei in certain growth/coverage models, we consider a Markov chain which has properties in common with related continuous-time Markov processes (as well as being of interest in its own right). We establish that the rate of convergence to normality for the number of ‘drops’ during times 1,2,…n is of the optimal ‘Berry–Esséen’ form, as n → ∞. We also establish a law of the iterated logarithm and a functional central limit theorem.

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4

Szewczak, Zbigniew S. "Berry–Esséen theorem for sample quantiles of asymptotically uncorrelated non reversible Markov chains." Communications in Statistics - Theory and Methods 46, no. 8 (2016): 3985–4003. http://dx.doi.org/10.1080/03610926.2015.1076478.

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5

Tu, D. S. "The Berry-esséen theorem for the subject-years method in mortality analysis with censored data." Metrika 38, no. 1 (1991): 269–83. http://dx.doi.org/10.1007/bf02613621.

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6

Dabrowski, AndréR, and Herold Dehling. "A Berry-Esséen theorem and a functional law of the iterated logarithm for weakly associated random vectors." Stochastic Processes and their Applications 30, no. 2 (1988): 277–89. http://dx.doi.org/10.1016/0304-4149(88)90089-0.

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7

Warren, Di. "The Frobenius–Harper technique in a general recurrence model." Journal of Applied Probability 36, no. 01 (1999): 30–47. http://dx.doi.org/10.1017/s002190020001682x.

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Abstract:

We present a general recurrence model which provides a conceptual framework for well-known problems such as ascents, peaks, turning points, Bernstein's urn model, the Eggenberger–Pólya urn model and the hypergeometric distribution. Moreover, we show that the Frobenius-Harper technique, based on real roots of a generating function, can be applied to this general recurrence model (under simple conditions), and so a Berry–Esséen bound and local limit theorems can be found. This provides a simple and unified approach to asymptotic theory for diverse problems hitherto treated separately.

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8

Warren, Di. "The Frobenius–Harper technique in a general recurrence model." Journal of Applied Probability 36, no. 1 (1999): 30–47. http://dx.doi.org/10.1239/jap/1032374227.

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Abstract:

We present a general recurrence model which provides a conceptual framework for well-known problems such as ascents, peaks, turning points, Bernstein's urn model, the Eggenberger–Pólya urn model and the hypergeometric distribution. Moreover, we show that the Frobenius-Harper technique, based on real roots of a generating function, can be applied to this general recurrence model (under simple conditions), and so a Berry–Esséen bound and local limit theorems can be found. This provides a simple and unified approach to asymptotic theory for diverse problems hitherto treated separately.

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9

Bentkus, V., and F. Götze. "On Minimal Moment Assumptions in Berry–Esséen Theorems for U-Statistics." Theory of Probability & Its Applications 40, no. 3 (1996): 430–45. http://dx.doi.org/10.1137/1140048.

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10

Samajder, Subhabrata, and Palash Sarkar. "Another look at normal approximations in cryptanalysis." Journal of Mathematical Cryptology 10, no. 2 (2016). http://dx.doi.org/10.1515/jmc-2016-0006.

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Abstract:

AbstractStatistical analysis of attacks on symmetric ciphers often requires assuming the normal behaviour of a test statistic. Typically such an assumption is made in an asymptotic sense. In this work, we consider concrete versions of some important normal approximations that have been made in the literature. To do this, we use the Berry–Esséen theorem to derive explicit bounds on the approximation errors. A basic mathematical requirement is that such approximation errors should be within reasonable bounds, a point which appears to have been overlooked in many of the earlier works on statistic

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