在生物多樣性的研究領域當中，兩個甚至到多個群落的比較是非常重要的研究議題，這類的生物多樣性被稱之為 生物多樣性。學者利用兩群落的總物種數目、特有種數目、共同種數目以及物種之間的相對豐富度定義了許多量化的指標，用以度量生物多樣性。當中較常被學者用來比較兩群落的多樣性指標有：Jaccard相似度指標、S□rensen相似度指標、Morisita相似度指標以及Shannon指標，這些指標在本文第二章的文獻回顧中都會詳盡的介紹其定義以及估計的方法。
本文主要針對Shannon型態的 多樣性指標作探討，主要分作三個部分，第一個部分推導出Shannon 多樣性指標的最大概似估計量的偏誤，第二部分利用Schechtman and Wang (2004)提出的兩階段摺刀法來修正最大概似估計量中的偏誤，並且利用電腦作模擬的方式，觀察摺刀估計量的表現。另一方面也用電腦模擬的方式，討論權數該作如何選擇，以及和Horvitz-Thompson估計量作比較。最後利用一組蝴蝶的資料以及哥斯大黎加雨林的資料作實例上的分析。

Arvesen, J. N. (1969). “Jackknifing U-Statistics”. The Annals of Mathematical Statistics, Vol. 40, No. 6, pp. 2076-2100.
Basharin, G. P. (1959). “On a Statistical Estimate for the Entropy of a Sequence of Independent Random Variable”. Theory of Probability and Its Applications, Vol4, pp.333-336
Chao, A. and Shen, T. J. (2003). “Nonparametric Estimation of Shannon's Index of Diversity When There are Unseen Species”. Environmental and Ecological Statistics, Vol.10, pp. 429-443
Efron, B. (1979). “Bootstrap Methods Another Look at the Jackknife”. The Annals of Statistics, Vol.7, No.1, pp. 1-26.
Good, I.J. (1953). “The Population Frequencies of Species and the Estimation of Population Parameters”. Biometrika, Vol.40, pp. 237-264.
Henry S. Horn. (1966). “Measurement of Overlap in Comparative Ecological Studies” .The American Naturalist, Vol. 100, No. 914 , pp. 419-424.
Hill, M.O. (1973). “Diversity and evenness: a unifying notation and its consequences.” Ecology, 54, 427-432.
Horvitz, D. G. and Thompson, D. J. (1952). “A Generalization of Sampling Without Replacement From a Finite Universe”. Journal of the American Statistical Association, Vol. 47, No. 260, pp. 663- 685
Jaccard, P. (1908). “Nouvelles researches sur la distribution florale”. Bull. Soc. Vaudoise Sci. Nat, Vol. 44, pp. 223-292.
Jost, L. (2006). “Entropy and diversity”. Oikos.113:2, pp.363-375.
Jost, L. (2007). “Partitioning Diversity into Independent Alpha and Beta Components”. Ecology, Vol. 88(10), pp. 2427–2439
Margules, C. R. and R. L. Pressey. (2000). “Systematic conservation planning”. Nature, 405: 243-253.
Morisita, M. (1959). “Measuring of interspecific association and similarity between communities”. Memoirs of the Faculty of Science, Kyushu Univ., Series E (Biology), Vol. 3, pp. 215-235.
Lande, R. (1996). “Statistics and partitioning of species diversity and similarity among multiple communities” .Oikos, 76, 5-13
Quenouille, M.H. (1956). “Notes on Bias in Estimation”. Biometrika, Vol. 43, No. 3/4, pp. 353-360.
Schechtman, E. and Wang, S. (2004) “Jackknifing two sample statistics. Journal of Statistical Planning and Inference”, Vol.119, 329-340
Shannon, C.E. (1948). “The mathematical theory of communication,” Bell System Technical Journal, 27, 379–423, 623–656
Simpson, E. H. (1949). “Measurement of diversity”. Nature, 163-688.
S□rensen, T. (1948). “A method of establishing groups of equal amplitude in plant sociology based on similarity of species and its application to analyses of the vegetation on Danish commons”. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab, Vol. 5 (4), pp. 1-34.
Whittaker, R.H. (1960). “Vegetation of the Siskiyou Mountains, Oregon and California” .Ecological Monograph, Vol.30, pp. 279-338
Wilson, M. V. and Shmida, A. (1984). “Measuring beta diversity with presence-absence data”. Journal of Ecology, 72, pp. 1055-1064
Zahl, S. (1977). “Jackknifing an index of diversity”. Ecology, Vol.58, 907-913
沈宗荏 (2003). “生物多樣性之預測” , 清華大學統計所博士論文
韓若平 (2008). “ Beta 多樣性的統計估計”, 清華大學統計所博士論文