The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. P. Baldi, Y. Rinott and C. Stein, A normal approximations for the number of local maxima of a random function on a graph, Probability, Statistics and Mathematics, Papers in Honor of Samuel Karlin, T. W. Anderson, K.B. Athreya and D. L. Iglehart eds. (1989), Academic Press, 59-81.
  2. D. Bayer and P. Diaconis, Trailing the dovetail shuffle to its lair, Ann. Appl. Probab. 2 (1992), no. 2, 294-313. MR1161056
  3. S. Chatterjee, Stein's method for concentration inequalities, Probab. Theory Related Fields 138 (2007), no. 1-2, 305-321. MR2288072
  4. S. Chatterjee, A new method of normal approximation, Ann. Probab. 36 (2008), no. 4, 1584-1610. MR2435859
  5. L.H.Y. Chen, L. Goldstein and Q.M. Shao. Normal Approximation by Stein's Method.(2010). Springer, New York.
  6. G. Englund, A remainder term estimate for the normal approximation in classical occupancy, Ann. Probab. 9 (1981), no. 4, 684-692. MR0624696
  7. Feller, W.(1966). An Introduction to Probability and its Applications, volume II. Wiley.
  8. S. Ghosh and L. Goldstein. Concentration of measures via size biased couplings, (2009). To appear in Probab. Th. Rel. Fields.
  9. L. Goldstein, Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing, J. Appl. Probab. 42 (2005), no. 3, 661-683. MR2157512
  10. L. Goldstein and M. D. Penrose, Normal approximation for coverage models over binomial point processes, Ann. Appl. Probab. 20 (2010), no. 2, 696-721. MR2650046
  11. L. Goldstein and Y. Rinott, Multivariate normal approximations by Stein's method and size bias couplings, J. Appl. Probab. 33 (1996), no. 1, 1-17. MR1371949
  12. P. Hall. Introduction to the theory of coverage processes, (1988). John Wiley, New York.
  13. V.F. Kolchin, B.A. Sevast'yanov and V.P. Chistyakov. Random Allocations, (1978). Winston, Washington D.C.
  14. M. Ledoux. The concentration of measure phenomenon, (2001). Amer. Math. Soc., Providence, RI.
  15. H. Luk. Stein's Method for the Gamma Distribution and Related Statistical Applications, Ph.D Thesis, (1994). Department of Mathematics, University of Southern California, USA.
  16. H. Midzuno, On the sampling system with probability proportionate to sum of sizes, Ann. Inst. Statist. Math., Tokyo 3 (1952), 99-107. MR0050840
  17. P. A. P. Moran, The random volume of interpenetrating spheres in space, J. Appl. Probab. 10 (1973), 483-490. MR0353412
  18. M. Penrose. Random geometric graphs, (2003). Oxford University Press, Oxford.
  19. M. D. Penrose, Normal approximation for isolated balls in an urn allocation model, Electron. J. Probab. 14 (2009), no. 74, 2156-2181. MR2550296
  20. M. D. Penrose and J. E. Yukich, Central limit theorems for some graphs in computational geometry, Ann. Appl. Probab. 11 (2001), no. 4, 1005-1041. MR1878288
  21. M. P. Quine and J. Robinson, A Berry-Esseen bound for an occupancy problem, Ann. Probab. 10 (1982), no. 3, 663-671. MR0659536
  22. M. Raic, CLT-related large deviation bounds based on Stein's method, Adv. in Appl. Probab. 39 (2007), no. 3, 731-752. MR2357379
  23. G. Reinert and A. Roellin, Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition, Ann. Probab. 37 (2009), no. 6, 2150-2173. MR2573554
  24. C. Stein. Approximate Computation of Expectations, (1986). Institute of Mathematical Statistics, Hayward, CA.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.