A Simulation Study of Two Biodiversity Index Estimation Procedures-In Comparing Bias Correction and Confidence Interval Coverage Rate
Date Issued
2006
Date
2006
Author(s)
Yang, Man-Hsia
DOI
zh-TW
Abstract
The most widely used measure of species diversity is Shannon index.
The traditional MLE method provides a biased estimator. The ML estimator tends to be underestimated,
especially when the number of unsampled specises increasing.
Chao and Pla proposed estimation methods that would adjust underestimated problems at almost the same time (Chao, December 2001, and Pla, May 2001).
Chao's estimation procedure combines the Horvise-Thompson(1952) adjustment for missing species and
the concept of sample coverage,
which is used to properly estimate the relative abundance of species discovered in the sample.
Pla proposed a technique using the difference of the original sample and
each bootstrap replication to constract an empirical adjustment for the bias,
and result in an adjusted point estimator and corresponding confidence interval.
Clearly, they used very different estimation procedures to estimate Shannon index.
In this study, we are interested in comparing the two estimation procedures in bias correction and
confidence interval coverage rate.
According to computer simulation results,
the two estimation procedures works well in adjusting underestimated in most conditions.
Only in small sample size and large diversity of relative abundance scenero,
the two estimation procedures are still underestimated, but less serious than MLE method.
Finally, we use four real examples to illustrate that
the two estimation procedures reveal the ability of adjusting underestimations.
They both have higher estimations than the traditional MLE method.
Pla used adjusted point estimation and the bootstrap standard deviation to estimat the adjusted confidence intervals.
The adjusted confidence interval coverage rate is highter than the standard percentile method and
corrected percentile technique, but still not provide the nominal coverage rate.
By computer simulation results, I discover that bootstrap variance is smaller than simulation variance.
Applying calbrating regression technique to adjust bootstrap variance allows us to recover the nominal coverage rate.
In four models and Venezuela simulations,
the adjusted variance by calibrating raises to a 90\% coverage.
Using adjusted variance to construct adjusted confidence intervals really can reach nomial coverage rate.
Subjects
生物多樣性指標
Shannon指標
biodiversity
Shannon index
Type
thesis
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