A sharp estimate of the binomial mean absolute deviation with applications

Statistics and Probability Letters

Volumn 83, Issue 4, 2013, Pages 1254-1259

  Berend, Daniel ^a   Kontorovich, Aryeh ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Binomial; Density estimation; Mean absolute deviation; Total variation

Indexed keywords

EID: 84874350059     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2013.01.023     Document Type: Article

References (13)

1. Berend, Daniel, Harremoës, Peter, Kontorovich, Aryeh, 2012. A reverse Pinsker inequality. Preprint.
2. Blyth Colin R. Expected absolute error of the usual estimator of the binomial parameter. Amer. Statist. 1980, 34(3):155-157.
3. Cover Thomas M., Thomas Joy A. Elements of Information Theory 2006, Wiley-Interscience, Hoboken, NJ. second ed.
4. den Hollander Frank Large Deviations. Fields Institute Monographs 2000, vol. 14. American Mathematical Society, Providence, RI.
5. Devroye Luc Exponential inequalities in nonparametric estimation. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 1991, vol. 335:31-44. Kluwer Acad. Publ., Dordrecht.
6. Diaconis Persi, Zabell Sandy Closed form summation for classical distributions: variations on a theme of de Moivre. Statist. Sci. 1991, 6(3):284-302.
7. Frame James S. Mean deviation of the binomial distribution. Amer. Math. Monthly 1945, 52(7):377-379.
8. Hsu Pao-Lu, Robbins Herbert Complete convergence and the law of large numbers. Proc. Natl. Acad. Sci. USA 1947, 33:25-31.
9. Johnson Norman L. A note on the mean deviation of the binomial distribution. Biometrika 1957, 44(3-4):532-533.
10. McDiarmid Colin On the method of bounded differences. LMS Lecture Notes Series 1989, vol. 141:148-188. Morgan Kaufmann Publishers, San Mateo, CA. J. Siemons (Ed.).
11. Orlitsky, Alon, 2012. Convergence of the empirical distribution. Private communication.
12. Pinelis Iosif F. Inequalities for distributions of sums of independent random vectors and their application to estimating a density. Teor. Veroyatn. Primen. 1990, 35(3):592-594.
13. Szarek Stanisław J. On the best constants in the Khinchin inequality. Studia Math. 1976, 58(2):197-208.