preseqR (version 4.0.0)

ds.rSAC.bootstrap: RFA estimator with bootstrap

Description

ds.rSAC.bootstrap predicts the expected number of species represented at least \(r\) times in a random sample, based on the initial sample.

Usage

ds.rSAC.bootstrap(n, r=1, mt=20, times=30, conf=0.95)

Arguments

n

A two-column matrix. The first column is the frequency \(j = 1,2,\dots\); and the second column is \(N_j\), the number of species with each species represented exactly \(j\) times in the initial sample. The first column must be sorted in an ascending order.

r

A positive integer. Default is 1.

mt

An positive integer constraining possible rational function approximations. Default is 20.

times

The number of bootstrap samples. Default is 30.

conf

The confidence level. Default is 0.95

Value

f

The estimator for the number of species represented at least \(r\) times in a random sample. The input of the estimator is a vector of sampling efforts t, i.e. the relative sample sizes comparing with the initial sample. For example, t = 2 means a random sample that is twice the size of the initial sample.

se

The standard error for the estimator. The input is a vector of sampling efforts \(t\).

lb

The lower bound of the confidence interval.The input is a vector of sampling efforts \(t\).

ub

The upper bound of the confidence interval.The input is a vector of sampling efforts \(t\).

Details

This is the bootstrap version of ds.rSAC. The bootstrap sample is generated by randomly sampling the initial sample with replacement. For each bootstrap sample, we construct an estimator. The median of estimates is used as the prediction for the number of species represented at least \(r\) times in a random sample.

The confidence interval is constructed based on a lognormal distribution.

References

Efron, B., & Tibshirani, R. J. (1994). An introduction to the bootstrap. CRC press.

Deng, C., Daley, T., Calabrese, P., Ren, J., & Smith, A.D. (2016). Estimating the number of species to attain sufficient representation in a random sample. arXiv preprint arXiv:1607.02804v3.

Examples

# NOT RUN {
## load library
# library(preseqR)

## import data
# data(FisherButterfly)

## construct the estimator for SAC
# ds1 <- ds.rSAC.bootstrap(FisherButterfly, r=1)
## The number of species represented at least once in a sample, 
## when the sample size is 10 or 20 times of the initial sample
# ds1$f(c(10, 20))
## The standard error of the estiamtes
# ds1$se(c(10, 20))
## The confidence interval of the estimates
# lb <- ds1$lb(c(10, 20))
# ub <- ds1$ub(c(10, 20))
# matrix(c(lb, ub), byrow=FALSE, ncol=2)

## construct the estimator for SAC
# ds2 <- ds.rSAC.bootstrap(FisherButterfly, r=2)
## The number of species represented at least twice in a sample, 
## when the sample size is 50 or 100 times of the initial sample
# ds2$f(c(50, 100))
## The standard error of the estiamtes
# ds2$se(c(50, 100))
## The confidence interval of the estimates
# lb <- ds2$lb(c(50, 100))
# ub <- ds2$ub(c(50, 100))
# matrix(c(lb, ub), byrow=FALSE, ncol=2)
# }