Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18723
標題: 連續型多樣性指標之模擬研究
A simulation study on continuous biodiversity indices
作者: 呂紫嫣
Lu, Tz-Yan
關鍵字: differential entropy

Shannon index
Bootstrap
kernel estimator
nearst neighbor estimator
m-spacing estimator
Shannon 指標
拔靴法
核估計
最近距離法
m-spacing估計
出版社: 統計學研究所
引用: Adams, J. E. and McCune, E. D. (1979), “Application of the Generalized jackknife to Shannon's Measure of Information Use as an Index of Diversity,” in In Ecological Diversity in Theory and Practice, eds. Grassle, J. F., Patil, G. P., Smith, W. and Taille, C., Fairland, Maryland:International Co-operative Publishing House, 117-131. Basharin, G P. (1959). “On a Statistical Estimate for the Entropy of a Sequence of Independent Random Variables,” Theory of Probaility and Its Applications 4, 333- 3 36. Beirlant, J. and Zuijlen, M. C. A.(1985). The empirical distribution function and strong la- ws for functions of order statistics of uniform spacings. J. Multivar. Anal. 16, 300- 317. Beirlant, J. (1986).Limit theory for spacing statistics from general univariate distributions. Pub. Inst. Stat. Univ. Paris XXXI fasc 1, 27-57. Blanco, J. M., Echevarría, F. and García, C. M. (1994). Dealing with size spectra: some conceptual and mathematical problems. Sci. Mar. 58(1-2):17-29. Bowman, A. W. and Azzalini, A. (1997). Applied smoothing techniques for data analysis: the kernel approach with S-plus illustration. Oxford Univ. Press. Cressie, N.(1976). On the logarithms of higher order spacings. Biometrika, 63, 343-355. Dudewicz, E.J. and van der Meulen, E.C. (1981).Entropy-based tests of uniformity. J. Amer. Statist. Assoc. 76, 967-974. Efron, B. (1979a). Bootstrap Methods: Another Look at the Jackknife. Annals of St- atist. 7,1-26. Efron, B., Tibshirani, R.J. (1993). An Introduction to the Bootstrap. Chapman & Hall, New York. Good, I J. (1953).The population frequencies of species and the estimation of population parameters. Biometrika 40:237-264. Hall, P.(1984). Limit theorems for sums of general functions of m-spacings. Math. Proc.Camb. Phil. Soc, 96, 517-532. Hall, P. (1986).On powerful distributional tests based on sample spacings. J. Multivariate Statist. 19, 201-225. Beirlant J., Dudewicz E.J., Gyorifi L.and van der Meulen, E.C. (2001). Nonparametric entropy estimation:an overview. Kerr, S. R. and Dickie, L.M. (2001). The biomass spectrum: a predator prey theory of aquatic production. Columbia Univerisity Press. Kozachenko, L. F. and Leonenko, N. N. (1987).Sample estimate of entropy of a random vector. Problems of Information Transmission, 23, 95-101 Lurie, D.,and Wagensberg, J. (1983). On biomass diversity in ecology. Bull. Math. Biol. 45(2):287-293. Miller, G. A. and Madow W. G. (1954), “On the Maximum Likelihood Estimate of the Shannon - Wiener Measure of Information,” AFCRC-TR-54-75,Air Force Cam- bridge Research Center, Air Research and Development Command, Bollong Air Fo- rce Base, Washington D.C. Robert, C. P. and G. Casella. (2000). Monte Carlo statistical methods. Springer. Ruiz, J. (1994. The measurement of size diversity in the pelagic ecosystem. Sci. mar. 58(1-2):103-107. Shannon, C.E. and Weaver, W. (1949). The mathematical theory of communicateon. Univ. of Illinois Press. Shen, T.-J. (2003), Predicitioin of Biodiversity, Ph.D. thesis , Institute of Statistics, National Tsing Hua Univerity. Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman & Hall. Simpson, E.H. (1949) Measurement of diverdity. Nature 163, 688. Strayer, D.L. (1991). Perspectives on the size structure of lacustrine zoobenthos, its causes, its consequences.J. North Am. Benthol. Soc. 10(2):210-221. Tsybakov, A. B. and van der Meulen, E. C.(1994). Root-n consistent estimators of entropy for densities with unbounded support. Scand. J. Statist., 23, 75-83. Van Es B. (1992)Estimating functionals related to a density by a class of statistics based on spacings. Scand. J. Statist. 19, 61-72. Vasicek O.(1976). A test for normality based on sample entropy. J. Roy. Statist. Soc. Ser. B 38, 54-59. Werner, E.E and Gillian, J.F. (1984). The ontogenetic niche and species interactions in size-structured populations. Xavier D. Quintana, Sandra Brucet , Dani Boix , Rocio Lopez-Flores , Stephanie Gascon, Anna Badosa, Jordi Sala, Ramon Moreno-Amich, and Juan J. Egozcue (2006). A nonparametric method for the measurement of size diversity with emphasis on data standardization. Limnology and oceanography:methods 6,75-86. Zahl, S. (1977), “Jackknifing an Index of Diversity,” Ecology 58, 907-913. http://www.ctfs.si.edu/
摘要: 測量生物多樣性指標,比較常用的有Simpson指標(1949)和Shannon指標(1948),常用來評估一群落中物種的組成和分布狀況,一般資料型態大都為離散型。但為了能更了解物種在生態系中的功能,或者在某些情況下資料並非離散型,例如:體重、體長……等,此時資料型態為連續的,因此傳統之多樣性指標並不適用。本文會回顧一些估計連續型Shannon指標的方法,以及試著使用拔靴法和Delta method去估計指標的標準差。最後本文利用電腦模擬評估各估計之表現。
Simpson index (Simpson, 1949) and Shannon index (Shannon, 1948) are two most widely used diversity indexes for measuring community structures. Most of diversity indexes in the literature are developed for dealing with categorical data (e.g. species counts). However, some research interest may focus on some variables with continuous type; for example, ecologists and biologists may concern the diversity regarding body sizes/weights of fishes, DBH's/heights of trees, etc. The present study is interested in evaluating some existing methods in the literature with such datasets. In addition, we have proposed some ways to construct the confidence intervals associated with those considered estimators. Based on the simulation study and data analysis with forest datasets, we have given some suggestions about the merits of the evaluated estimators.
URI: http://hdl.handle.net/11455/18723
其他識別: U0005-1107201112330300
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-1107201112330300
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