Open Access
Issue |
ESAIM: PS
Volume 25, 2021
|
|
---|---|---|
Page(s) | 325 - 345 | |
DOI | https://doi.org/10.1051/ps/2021012 | |
Published online | 27 July 2021 |
- B. Arras and C. Houdré, On Stein’s method for infinitely divisible laws with finite first moment. Springer Briefs in Probability and Mathematical Statistics. Springer, Cham (2019). [Google Scholar]
- A.C. Berry, The accuracy of the Gaussian approximation to the sum of independent variates. Trans. Am. Math. Soc. 49 (1941) 122–136. [Google Scholar]
- A. Braverman and J.G. Dai, High order steady-state diffusion approximation of the Erlang-C system. Preprint arXiv:1602.02866 (2016). [Google Scholar]
- L.H.Y. Chen and Q.-M. Shao, Stein’s method for normal approximation, in Vol. 4 of Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. Singapore Univ. Press, Singapore (2005) 1–59. [Google Scholar]
- F. Daly, Upper bounds for Stein-type operators. Electon. J. Probab. 13 (2008) 566–587. [Google Scholar]
- C. Döbler, Stein’s method of exchangeable pairs for the beta distribution and generalizations. Electr. J. Probab. 20 (2015) 1–34. [Google Scholar]
- C. Döbler, Distributional transformations without orthogonality relations. J. Theor. Probab. 30 (2017) 85–116. [Google Scholar]
- C. Döbler, R.E. Gaunt and S.J. Vollmer, An iterative technique for bounding derivatives of solutions of Stein equations. Electr. J. Probab. 22 (2017) 1–39. [Google Scholar]
- L. Döbler, R. Samworth and J. Wellner, Bounding distributional errors via density ratios. Preprint arXiv:1905.03009 (2019). [Google Scholar]
- M. Ernst, G. Reinert and Y. Swan, First order covariance inequalities via Stein’s method. To appear in Bernoulli (2020). [Google Scholar]
- M. Ernst and Y. Swan, Distances between distributions via Stein’s method. Preprint arXiv:1909.11518 (2019). [Google Scholar]
- C.G. Esseen, On the Liapunoff limit of error in the theory of probability. Ark. Mat. Astron. Fys. A28 (1942) 1–19. [Google Scholar]
- M. Fathi, Higher-order Stein kernels for Gaussian approximation. To appear in Stud. Math. (2020). [Google Scholar]
- W. Feller, On the Berry-Esseen Theorem. Z. Wahrscheinlichkeit 10 (1968) 261–268. [Google Scholar]
- R.E. Gaunt, Variance-Gamma approximation via Stein’s method. Electr. J. Probab. 19 (2014) 1–33. [Google Scholar]
- R.E. Gaunt, Rates of convergence in normal approximation under moment conditions via new bounds on solutions of the Stein equation. J. Theor. Probab. 29 (2016) 231–247. [Google Scholar]
- R.E. Gaunt, Products of normal, beta and gamma random variables: Stein operators and distributional theory. Braz. J. Probab. Stat. 32 (2018) 437–466. [Google Scholar]
- R.E. Gaunt Wasserstein and Kolmogorov error bounds for variance-gamma approximation via Stein’s method I. J. Theor. Probab. 33 (2020) 465–505. [Google Scholar]
- R.E. Gaunt Stein’s method for functions of multivariate normal random variables. Ann. Inst. Henri Poincaré Prob. Stat. 56 (2020) 1484–1513. [Google Scholar]
- R.E. Gaunt, G. Mijoule, and Y. Swan, An algebra of Stein operators. J. Math. Anal. Appl. 469 (2019) 260–279. [Google Scholar]
- R.E. Gaunt, A.M. Pickett and G. Reinert, Chi-square approximation by Stein’s method with application to Pearson’s statistic. Ann. Appl. Probab. 27 (2017) 720–756. [Google Scholar]
- L. Goldstein and G. Reinert, Stein’s Method and the zero bias transformation with application to simple random sampling. Ann. Appl. Probab. 7 (1997) 935–952. [Google Scholar]
- L. Goldstein and G. Reinert, Stein’s method for the Beta distribution and the Pólya-Eggenberger Urn. J. Appl. Probab. 50 (2013) 1187–1205. [Google Scholar]
- M.E.H. Ismail, L. Lorch and M.E. Muldoon, Completely monotonic functions associated with the gamma function and its q-analogues. J. Math. Anal. Appl. 116 (1986) 1–9. [Google Scholar]
- A.V. Kakosyan, L.B. Klebanov and I.A. Melamed, Characterization of Distributions by the Method of Intensively Monotone Operators, Vol. 1088 of Lecture Notes in Math. Springer, Berlin (1984). [Google Scholar]
- V. Kalashnikov, Geometric Sums: Bounds for Rare Events with Applications. Risk Analysis, Reliability, Queueing. Kluwer Academic Publishers Group, Dordrecht (1997). [Google Scholar]
- E. Konzou and A. Koudou, About the Stein equation for the generalized inverse Gaussian and Kummer distributions. ESAIM: PS 24 (2020) 607–626. [EDP Sciences] [Google Scholar]
- S. Kotz, T.J. Kozubowski and K. Podgórski, The Laplace Distribution and Generalizations: A Revisit with New Applications. Springer (2001). [Google Scholar]
- C. Lefèvre and S. Utev, Exact norms of a Stein-type operator and associated stochastic orderings. Probab. Theory Rel. 127 (2003) 353–366. [Google Scholar]
- C. Ley, G. Reinert and Y. Swan, Stein’s method for comparison of univariate distributions. Probab. Surv. 14 (2017) 1–52. [Google Scholar]
- H. Luk, Stein’s Method for the Gamma Distribution and Related Statistical Applications. Ph.D. thesis, University of Southern California (1994). [Google Scholar]
- F.W.J. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark, NIST Handbook of Mathematical Functions. Cambridge University Press (2010). [Google Scholar]
- A.G. Pakes, A characterization of gamma mixtures of stable laws motivated by limit theorems. Stat. Neerl. 46 (1992) 209–218. [Google Scholar]
- A.G. Pakes, On characterizations through mixed sums. Aust. J. Stat. 34 (1992) 323–339. [Google Scholar]
- E. Peköz and A. Röllin, New rates for exponential approximation and the theorems of Rényi and Yaglom. Ann. Probab. 39 (2011) 587–608. [Google Scholar]
- E. Peköz, A. Röllin and N. Ross, Total variation error bounds for geometric approximation. Bernoulli 19 (2013) 610–632. [Google Scholar]
- E. Peköz, A. Röllin and N. Ross, Exponential and Laplace approximation for occupation statistics of branching random walk. Electr. J. Probab. 25 (2020) 1–22. [Google Scholar]
- J. Pike and H. Ren, Stein’s method and the Laplace distribution. ALEA Lat. Am. J. Probab. Math. Stat. 11 (2014) 571–587. [Google Scholar]
- G. Reinert, Couplings for normal approximations with Stein’s method, in Microsurveys in Discrete Probability, volume of DIMACS series AMS (1998) 193–207. [Google Scholar]
- A. Rényi, A characterization of Poisson processes. Magyar Tud. Akad. Mat. Kutató Int. Közl. 1 (1957) 519–527. [Google Scholar]
- W. Schoutens, Orthogonal Polynomials in Steins Method. EURANDOM Report 99-041, EURANDOM, 1999. [Google Scholar]
- W. Schoutens, Orthogonal polynomials in Stein’s method. J. Math. Anal. Appl. 253 (2001) 515–531. [Google Scholar]
- I. Shevtsova, An improvement of convergence rate estimates in the Lyapunov theorem. Dokl. Math. 253 (2010) 862–864. [Google Scholar]
- I. Shevtsova, On the absolute constants in the Berry Esseen type inequalities for identically distributed summands. Preprint arXiv:1111.6554 (2011). [Google Scholar]
- C. Stein, A bound for the error in the normal approximation to the the distribution of a sum of dependent random variables. Vol. 2 of Proc. Sixth Berkeley Symp. Math. Statis. Prob. Univ. California Press, Berkeley (1972) 583–602. [Google Scholar]
- C. Stein, Approximate Computation of Expectations. IMS, Hayward, California (1986). [Google Scholar]
- A.A. Toda, Weak limit of the geometric sum of independent but not identically distributed random variables. Preprint arXiv:1111.1786 (2011). [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.