Research Article
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Year 2020, Volume: 33 Issue: 1, 229 - 236, 01.03.2020
https://doi.org/10.35378/gujs.554644

Abstract

References

  • [1] Batten, L. A., “Bird communities of some Killarney woodlands”, Proceedings of the Royal Irish Academy. Section B: Biological, geological, and chemical science. Royal Irish Academy, 76: 285-313, (1976).
  • [2] Bonachela, Juan A., Haye Hinrichsen and Miguel A. Munoz, “Entropy estimates of small data sets”, Journal of Physics A: Mathematical and Theoretical, 41(20): 1-9, (2008).
  • [3] Li, Y. and Busch, P., “Von Neumann entropy and majorization”, Journal of Mathematical Analysis and Applications 408(1): 384–393, (2013).
  • [4] Chao, A. and Lee, S.M., “Estimating the number of classes via sample coverage”, Journal of the American statistical Association, 87(417): 210-217, (1992).
  • [5] Chao, A., Ma, M.C., Yang, M.C., “Stopping rules and estimation for recapture debugging with unequal failure rates”, Biometrika, 80(1): 193-201 (1993).
  • [6] Chao, A., Hwang, W.H., Chen, Y.C., Kuo, C.Y., “Estimating the number of shared species in two communities”, Statistica sinica, 10: 227-246, (2000).
  • [7] Chao, A., Shen, T.J., “Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample”, Environmental and Ecological Statistics, 10(4): 429-443, (2003).
  • [8] Chao, A., Wang, Y.T., Jost, L., “Entropy and the species accumulation curve: a novel entropy estimator via discovery rates of new species”, Methods in Ecology and Evolution , 4(11): 1091-1100, (2013).
  • [9] Chao, A., Chiu, C.H., “Species richness: estimation and comparison”, Wiley StatsRef: Statistical Reference Online, 1-26, (2016).
  • [10] Chiu, C.H., Wang, Y.T., Walther, B.A., Chao, A., “An improved nonparametric lower bound of species richness via a modified Good–Turing frequency formula”, Biometrics, 70: 671-682, (2014).
  • [11] Gorelick, R., “Combining richness and abundance into a single diversity index using matrix analogues of Shannon’s and Simpson’s indices”, Ecography, 29: 525-530, (2006).
  • [12] Grassberger, P., “Finite sample corrections to entropy and dimension estimates”, Physics Letters A, 128(6-7): 369-373, (1988).
  • [13] Grassberger, P., “Entropy Estimates from Insufficient Samplings”, ArXiv Physics e-prints, 0307138, (2003).
  • [14] Holst, L., “Some asymptotic results for incomplete multinomial or Poisson samples”, Scandinavian Journal of Statistics, 8: 243-246, (1981).
  • [15] Holste, D., Grosse, I., Herzel, H., “Bayes' estimators of generalized entropies”, Journal of Physics A: Mathematical and General, 31(11): 2551-2566, (1998).
  • [16] Janzen, D.H., “Sweep samples of tropical foliage insects: description of study sites, with data on species abundances and size distributions”, Ecology, 54(3): 659-686, (1973a).
  • [17] Janzen, D.H., “Sweep samples of tropical foliage insects: effects of seasons, vegetation types, elevation, time of day, and insularity”, Ecology, 54(3): 687-708, (1973b).
  • [18] Miller, G., “Note on the bias of information estimates”, Information Theory in Psychology: Problems and Methods, 95-100, (1955).
  • [19] Schurmann, T., “Bias analysis in entropy estimation”, Journal of Physics A: Mathematical and Theoretical, 37(27): L295-L301, (2004).
  • [20] Shannon, C. E., “A mathematical theory of communication”, Bell System Technical Journal, 27(3): 379-423, (1948).
  • [21] Zahl, S., “Jackknifing an index of diversity”, Ecology, 58(4): 907-913, (1977).
  • [22] Zhang, Z., “Entropy Estimation in Turing's Perspective”, Neural Computation, 24(5): 1368-1389, (2012).

A New Proposed Estimator for Reducing Bias Due to Undetected Species

Year 2020, Volume: 33 Issue: 1, 229 - 236, 01.03.2020
https://doi.org/10.35378/gujs.554644

Abstract

The present paper addresses a new approach to reduce
bias when there are undetected species in a plot. Partially density matrix plays essential role in this new proposed
estimator. The performance of the new proposed estimator 
(Ĥ0was compared to bias-corrected MLE (MLEBC), Jackknife (JK) and the proposed estimator of Chao and Shen cs using Principle component analysis (PCA). The
result of the first PCA applied to the data including the estimators’ values of
the assemblages showed that
 Ĥ0 is located
between JK and 
Ĥcs and its’ nearest neighbor becomes JK. The
second PCA was applied to the data belonging to the relative estimator values
between the pairwise assemblages and, it was found that 
Ĥ0 is still
located between JK and 
Ĥcs but its’ nearest neighbor becomes Ĥcs in this time
along the first axis. Those results were evaluated that 
Ĥ0 is a better
estimator than MLE
BC. Thus the new proposed estimator (
Ĥ0can also be used as an alternative
bias-corrected estimator in addition to the other estimators.

References

  • [1] Batten, L. A., “Bird communities of some Killarney woodlands”, Proceedings of the Royal Irish Academy. Section B: Biological, geological, and chemical science. Royal Irish Academy, 76: 285-313, (1976).
  • [2] Bonachela, Juan A., Haye Hinrichsen and Miguel A. Munoz, “Entropy estimates of small data sets”, Journal of Physics A: Mathematical and Theoretical, 41(20): 1-9, (2008).
  • [3] Li, Y. and Busch, P., “Von Neumann entropy and majorization”, Journal of Mathematical Analysis and Applications 408(1): 384–393, (2013).
  • [4] Chao, A. and Lee, S.M., “Estimating the number of classes via sample coverage”, Journal of the American statistical Association, 87(417): 210-217, (1992).
  • [5] Chao, A., Ma, M.C., Yang, M.C., “Stopping rules and estimation for recapture debugging with unequal failure rates”, Biometrika, 80(1): 193-201 (1993).
  • [6] Chao, A., Hwang, W.H., Chen, Y.C., Kuo, C.Y., “Estimating the number of shared species in two communities”, Statistica sinica, 10: 227-246, (2000).
  • [7] Chao, A., Shen, T.J., “Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample”, Environmental and Ecological Statistics, 10(4): 429-443, (2003).
  • [8] Chao, A., Wang, Y.T., Jost, L., “Entropy and the species accumulation curve: a novel entropy estimator via discovery rates of new species”, Methods in Ecology and Evolution , 4(11): 1091-1100, (2013).
  • [9] Chao, A., Chiu, C.H., “Species richness: estimation and comparison”, Wiley StatsRef: Statistical Reference Online, 1-26, (2016).
  • [10] Chiu, C.H., Wang, Y.T., Walther, B.A., Chao, A., “An improved nonparametric lower bound of species richness via a modified Good–Turing frequency formula”, Biometrics, 70: 671-682, (2014).
  • [11] Gorelick, R., “Combining richness and abundance into a single diversity index using matrix analogues of Shannon’s and Simpson’s indices”, Ecography, 29: 525-530, (2006).
  • [12] Grassberger, P., “Finite sample corrections to entropy and dimension estimates”, Physics Letters A, 128(6-7): 369-373, (1988).
  • [13] Grassberger, P., “Entropy Estimates from Insufficient Samplings”, ArXiv Physics e-prints, 0307138, (2003).
  • [14] Holst, L., “Some asymptotic results for incomplete multinomial or Poisson samples”, Scandinavian Journal of Statistics, 8: 243-246, (1981).
  • [15] Holste, D., Grosse, I., Herzel, H., “Bayes' estimators of generalized entropies”, Journal of Physics A: Mathematical and General, 31(11): 2551-2566, (1998).
  • [16] Janzen, D.H., “Sweep samples of tropical foliage insects: description of study sites, with data on species abundances and size distributions”, Ecology, 54(3): 659-686, (1973a).
  • [17] Janzen, D.H., “Sweep samples of tropical foliage insects: effects of seasons, vegetation types, elevation, time of day, and insularity”, Ecology, 54(3): 687-708, (1973b).
  • [18] Miller, G., “Note on the bias of information estimates”, Information Theory in Psychology: Problems and Methods, 95-100, (1955).
  • [19] Schurmann, T., “Bias analysis in entropy estimation”, Journal of Physics A: Mathematical and Theoretical, 37(27): L295-L301, (2004).
  • [20] Shannon, C. E., “A mathematical theory of communication”, Bell System Technical Journal, 27(3): 379-423, (1948).
  • [21] Zahl, S., “Jackknifing an index of diversity”, Ecology, 58(4): 907-913, (1977).
  • [22] Zhang, Z., “Entropy Estimation in Turing's Perspective”, Neural Computation, 24(5): 1368-1389, (2012).
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Statistics
Authors

Kürşad Özkan 0000-0002-8526-7243

Publication Date March 1, 2020
Published in Issue Year 2020 Volume: 33 Issue: 1

Cite

APA Özkan, K. (2020). A New Proposed Estimator for Reducing Bias Due to Undetected Species. Gazi University Journal of Science, 33(1), 229-236. https://doi.org/10.35378/gujs.554644
AMA Özkan K. A New Proposed Estimator for Reducing Bias Due to Undetected Species. Gazi University Journal of Science. March 2020;33(1):229-236. doi:10.35378/gujs.554644
Chicago Özkan, Kürşad. “A New Proposed Estimator for Reducing Bias Due to Undetected Species”. Gazi University Journal of Science 33, no. 1 (March 2020): 229-36. https://doi.org/10.35378/gujs.554644.
EndNote Özkan K (March 1, 2020) A New Proposed Estimator for Reducing Bias Due to Undetected Species. Gazi University Journal of Science 33 1 229–236.
IEEE K. Özkan, “A New Proposed Estimator for Reducing Bias Due to Undetected Species”, Gazi University Journal of Science, vol. 33, no. 1, pp. 229–236, 2020, doi: 10.35378/gujs.554644.
ISNAD Özkan, Kürşad. “A New Proposed Estimator for Reducing Bias Due to Undetected Species”. Gazi University Journal of Science 33/1 (March 2020), 229-236. https://doi.org/10.35378/gujs.554644.
JAMA Özkan K. A New Proposed Estimator for Reducing Bias Due to Undetected Species. Gazi University Journal of Science. 2020;33:229–236.
MLA Özkan, Kürşad. “A New Proposed Estimator for Reducing Bias Due to Undetected Species”. Gazi University Journal of Science, vol. 33, no. 1, 2020, pp. 229-36, doi:10.35378/gujs.554644.
Vancouver Özkan K. A New Proposed Estimator for Reducing Bias Due to Undetected Species. Gazi University Journal of Science. 2020;33(1):229-36.