estimatepopulation {SparseMSE}

Bootstrapping to evaluate confidence intervals using BCa methods

Description

This routine implements the bootstrapping and jacknife approach as detailed in Section 3.3 of Chan, Silverman and Vincent (2019). It calls the routine estimatepopulation.0 and so is the preferred routine to be called if a user wishes to estimate the population and obtain BCa confidence intervals.

Usage

estimatepopulation(zdat, nboot = 1000, pthresh = 0.02, iseed = 1234,
  alpha = c(0.025, 0.05, 0.1, 0.16, 0.84, 0.9, 0.95, 0.975), ...)

Arguments

zdat

Data matrix with t+1 columns. The first t columns, each corresponding to a particular list, are 0s and 1s defining the capture histories observed. The last column is the count of cases with that particular capture history. List names A, B, ... are constructed if not supplied. Where a capture history is not explicitly listed, it is assumed that it has zero count.

nboot

Number of bootstrap replications.

pthresh

p-value threshold used in estimatepopulation.0.

iseed

seed for initialisation.

alpha

Bootstrap quantiles of interests.

...

other arguments which will be passed to estimatepopulation.0

Value

A list with components as below:

popest point estimate of the total population of the original data set

MSEfit model fitted to the data, in the format described in modelfit

bootreps point estimates of total population sizes from each bootstrap sample

ahat the estimated acceleration factor

BCaquantiles BCa confidence intervals

References

Chan, L., Silverman, B. W., and Vincent, K. (2019). Multiple Systems Estimation for Sparse Capture Data: Inferential Challenges when there are Non-Overlapping Lists. Available from https://arxiv.org/abs/1902.05156.

DiCiccio, T. J. and Efron, B. (1996). Bootstrap Confidence Intervals. Statistical Science, 40(3), 189-228.