Re-parameterization of multinomial distributions and diversity indices

Zhang, Zhiyi; Zhou, Jun

doi:10.1016/j.jspi.2009.12.023

Cited by 34 publications

(34 citation statements)

References 13 publications

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“…According to Zhang and Zhou [12], for every v with 1 ≤ v ≤ n − 1, Z 1,v , as given in Equation (5), is the uniformly minimum variance unbiased estimator (umvue) of…”

Section: Bias Adjustmentmentioning

confidence: 99%

Bias Adjustment for a Nonparametric Entropy Estimator

Zhang

Grabchak

2013

Entropy

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Zhang in 2012 introduced a nonparametric estimator of Shannon's entropy, whose bias decays exponentially fast when the alphabet is finite. We propose a methodology to estimate the bias of this estimator. We then use it to construct a new estimator of entropy. Simulation results suggest that this bias adjusted estimator has a significantly lower bias than many other commonly used estimators. We consider both the case when the alphabet is finite and when it is countably infinite.

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“…According to Zhang and Zhou [12], for every v with 1 ≤ v ≤ n − 1, Z 1,v , as given in Equation (5), is the uniformly minimum variance unbiased estimator (umvue) of…”

Section: Bias Adjustmentmentioning

confidence: 99%

Bias Adjustment for a Nonparametric Entropy Estimator

Zhang

Grabchak

2013

Entropy

Self Cite

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“…Despite the prevalence of α-and β-diversity analyses in ecology, statistical methodology to estimate these functions is relatively underdeveloped. In particular, much of the existing literature focuses on estimating diversity under the assumption of observations drawn from a multinomial distribution with unknown probability vector z (Miller 1955, Zahl 1977, Zhang & Zhou 2010, Hsieh et al 2016, Cao et al 2017. Fortunately, there exist sophisticated models for community composition data that permit more a flexible co-occurrence structure than that implied by the multinomial distribution.…”

Section: Introductionmentioning

confidence: 99%

DivNet: Estimating diversity in networked communities

Willis¹,

Bd²

2018

Preprint

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Diversity is a marker of ecosystem health in ecology, microbiology and immunology, with implications for disease diagnosis and infection resistance. However, accurately comparing diversity across environmental gradients is challenging, especially when number of different taxonomic groups in the community is large. Furthermore, existing approaches to estimating diversity do not perform well when the taxonomic groups in the community interact via an ecological network, such as by competing within their niche, or with mutualistic relationships. To address this, we propose DivNet, a method for estimating within-and between-community diversity in ecosystems where taxa interact via an ecological network. In particular, accounting for network structure permits more accurate estimates of alphaand beta-diversity, even in settings with a large number of taxa and a small number of samples. DivNet is fast, accurate, precise, performs well with large numbers of taxa, and is robust to both weakly and strongly networked communities. We show that the advantages of incorporating taxon interactions into diversity estimation are especially clear in analyzing microbiomes and other high-diversity, strongly networked ecosystems. Therefore, to illustrate the method, we analyze the microbiome of seafloor basalts based on a 16S amplicon sequencing dataset with 1490 taxa and 13 samples.

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“…Practical techniques include jackknife and bootstrap, see Fritsch and Hsu (1999). Zhang and Zhou (2010) studied a group of estimators for ζ u,v . Due to these problems, little is known about the asymptotic distributional characteristics except in a naive approach.…”

Section: Introductionmentioning

confidence: 99%

A new diversity estimator

Zheng

Jiang

2017

J Stat Distrib App

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The maximum likelihood estimator (MLE) of Gini-Simpson's diversity index (GS) is widely used but suffers from large bias when the number of species is large or infinite. We propose a new estimator of the GS index and show its unbiasedness. Asymptotic normality of the proposed estimator is established when the number of species in the population is finite and known, finite but unknown, and infinite. Simulations demonstrate advantages of our estimator over the MLE, and a real example for the extinction of dinosaurs endorses the use of our approach. Mathematics Subject Classification (MSC) codes is 60E05, which refers to distributions: general theory.

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Re-parameterization of multinomial distributions and diversity indices

Cited by 34 publications

References 13 publications

Bias Adjustment for a Nonparametric Entropy Estimator

Bias Adjustment for a Nonparametric Entropy Estimator

DivNet: Estimating diversity in networked communities

A new diversity estimator

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