Bernoulli

  • Bernoulli
  • Volume 16, Number 2 (2010), 493-513.

Estimation of a probability with optimum guaranteed confidence in inverse binomial sampling

Luis Mendo and José M. Hernando

Full-text: Open access

Abstract

Sequential estimation of a probability p by means of inverse binomial sampling is considered. For μ1, μ2>1 given, the accuracy of an estimator ̂p is measured by the confidence level P[p/μ2̂p1]. The confidence levels c0 that can be guaranteed for p unknown, that is, such that P[p/μ2̂p1]≥c0 for all p∈(0, 1), are investigated. It is shown that within the general class of randomized or non-randomized estimators based on inverse binomial sampling, there is a maximum c0 that can be guaranteed for arbitrary p. A non-randomized estimator is given that achieves this maximum guaranteed confidence under mild conditions on μ1, μ2.

Article information

Source
Bernoulli, Volume 16, Number 2 (2010), 493-513.

Dates
First available in Project Euclid: 25 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1274821081

Digital Object Identifier
doi:10.3150/09-BEJ219

Mathematical Reviews number (MathSciNet)
MR2668912

Zentralblatt MATH identifier
1323.62082

Keywords
confidence level interval estimation inverse binomial sampling sequential estimation

Citation

Mendo, Luis; Hernando, José M. Estimation of a probability with optimum guaranteed confidence in inverse binomial sampling. Bernoulli 16 (2010), no. 2, 493--513. doi:10.3150/09-BEJ219. https://projecteuclid.org/euclid.bj/1274821081


Export citation

References

  • Abramowitz, M. and Stegun, I.A., eds. (1970). Handbook of Mathematical Functions, 9th ed. New York: Dover.
  • Chen, X. (2007). Inverse sampling for nonasymptotic sequential estimation of bounded variable means. Available at arXiv:0711.2801v2 [math.ST].
  • Haldane, J.B.S. (1945). On a method of estimating frequencies. Biometrika 33 222–225.
  • Lehmann, E.L. and Casella, G. (1998). Theory of Point Estimation, 2nd ed. New York: Springer.
  • Mendo, L. and Hernando, J.M. (2006). A simple sequential stopping rule for Monte Carlo simulation. IEEE Trans. Commun. 54 231–241.
  • Mendo, L. and Hernando, J.M. (2008a). Improved sequential stopping rule for Monte Carlo simulation. IEEE Trans. Commun. 56 1761–1764.
  • Mendo, L. and Hernando, J.M. (2008b). Unbiased Monte Carlo estimator with guaranteed confidence. In Proc. IEEE Int. Workshop on Signal Processing Advances in Wireless Communications 625–628. New York: IEEE.
  • Mikulski, P.W. and Smith, P.J. (1976). A variance bound for unbiased estimation in inverse sampling. Biometrika 63 216–217.
  • Papoulis, A. and Pillai, S.U. (2002). Probability, Random Variables and Stochastic Processes, 4th ed. New York: McGraw-Hill.
  • Petkovšek, M., Wilf, H.S. and Zeilberger, D. (1996). A=B. Wellesley: Peters.
  • Prasad, G. and Sahai, A. (1982). Sharper variance upper bound for unbiased estimation in inverse sampling. Biometrika 69 286.
  • Sathe, Y.S. (1977). Sharper variance bounds for unbiased estimation in inverse sampling. Biometrika 64 425–426.