Communications for Statistical Applications and Methods

  • 제18권4호
  • /
  • Pages.457-465
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  • 2011
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Improving Sample Entropy Based on Nonparametric Quantile Estimation

  • 투고 : 20110300
  • 심사 : 20110500
  • 발행 : 2011.07.31
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초록

Sample entropy (Vasicek, 1976) has poor performance, and several nonparametric entropy estimators have been proposed as alternatives. In this paper, we consider a piecewise uniform density function based on quantiles, which enables us to evaluate entropy in each interval, and study the poor performance of the sample entropy in terms of the poor estimation of lower and upper quantiles. Then we propose some improved entropy estimators by simply modifying the quantile estimators, and compare their performances with some existing estimators.

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참고문헌

  1. Ahmad, I. A. and Lin, P. E. (1976). A nonparametric estimation of the entropy for absolutely continuous distributions, IEEE Transactions on Information Theory, 22, 372-375. https://doi.org/10.1109/TIT.1976.1055550
  2. Bowman, A. W. (1992). Density based tests for goodness-of-fit, Journal of Statistical Computation and Simulation, 40, 1-13. https://doi.org/10.1080/00949659208811361
  3. Choi, B. and Kim, K. (2006). Testing goodness of fit for Laplace distribution based on maximum entropy, Statistics, 40, 517-531. https://doi.org/10.1080/02331880600822473
  4. Correa, J. C. (1995). A new estimator of entropy, Communications in Statistics: Theory and Method, 24, 2439-2449 https://doi.org/10.1080/03610929508831626
  5. Dmitriev, Y. G. and Tarasenko, F. P. (1973). On the estimation of functionals of the probability density and its derivatives, Theory of Probability and its Applications, 18, 628-633.
  6. Dudewicz, E. and van der Meulen, E. (1987). The empiric entropy, a new approach to nonparametric entropy estimation, New Prospectives in Theoretical and Applied Statistics, 207-227.
  7. Ebrahimi, N., Pflughoeft, K. and Soofi, E. S. (1994). Two measures of sample entropy, Statistics and Probability Letters, 20, 225-234. https://doi.org/10.1016/0167-7152(94)90046-9
  8. Park, S. and Park, D. (2003). Correcting moments for goodness of fit tests based on two entropy estimates, Journal of Statistical Computation and Simulation, 73, 685-694. https://doi.org/10.1080/0094965031000070367
  9. Reiss, R. D. (1981). Nonparametric estimation of smooth distribution functions, Scandinavian Journal of Statistics, 8, 116-119.
  10. Shannon, C. E. (1948). A mathematical theory of communications, Bell System Technical Journal, 27, 379-423, 623-656. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  11. Theil, H. (1980). The entropy of the maximum entropy distribution, Economics Letters, 5, 145-148. https://doi.org/10.1016/0165-1765(80)90089-0
  12. Vasicek, O. (1976). A test for normality based on sample entropy, Journal of the Royal Statistical Society, Series B, 38, 54-59.
  13. Yang, S. S. (1985). A smooth nonparametric estimator of a quantile function, Journal of American Statistical Association, 80, 1004-1011. https://doi.org/10.2307/2288567