extWeibQuant (version 1.1)

bootstrapCMLE: Bootstrap Censored Weibull MLE for censoring threshold selection and standard error of the quantile estimates

Description

Proposed in Chapter 5 of Liu (2012). The original data set will be bootstrapped to obtain an estimate of the mean squared error of the quantile estimates, such that quantile estimates under different subjective censoring thresholds could be compared. We could also obtain the standard error of quantile estimates via bootstrap.

Usage

bootstrapCMLE(dat, qInt = 0.05, canSet = seq(0.1, 0.5, by = 0.1), 
			B = 5000, randSeed = NULL, conCr = 1e-09, nIter = 1000)

Arguments

dat

A complete data set without censoring. See Details

qInt

The quantile of interest, e.g. 5% quantile or 10% quantile.

canSet

A vector of the candidate subjective censoring thresholds, expressed as the proportion of data smaller it, e.g. 10%, 20%, ..., 100% (non-censoring)

B

Number of bootstrap replicate data sets

randSeed

The seed for random number generation. If NULL, the random seed will not be set

conCr

Convergence criterion for the algorithm to calculate the censored Weibull MLE. See cenWbMLE.T1

nIter

See cenWbMLE.T1

Value

results

A matrix of length(canSet) by six. The first column is the candidate threshold (proportion). The second and third column is the parameter estimates of the Weibull model for the original data set. The fourth column is the quantile estimate under this censoring threshold. The fifth column and sixth column are the bootstrap estimate of the standard error (SE) and root mean squared error (RMSE) of this quantile estimate.

bQEst

A matrix of B-by-length(canSet). The quantile estimates under each censoring threshold for each bootstrap replicate.

Details

This function is designed to only work for a complete data set where every observation is fully observed (non-censoring). We could decide the best threshold (proportion) of subjective censoring based on bootstrap. For the advantage of subjective censoring, please see Liu (2012).

This function will call C to do all calculations. So it is recommended that the user should make sure the cenWbMLE.T2 could work for their original data set.

References

Liu Y. (2012). Lower Quantile Estimation of Wood Strength Data. Master Thesis, Department of Statistics, UBC. Downloadable here.

See Also

bootstrapCenWbMix

Examples

set.seed(1)
y <- sort(rweibull(100, 7, 7))
tlist <- bootstrapCMLE(y, B=1000, canSet=c(0.1, 0.5, 1), randSeed=1)
tlist$results #Usually, we only need to look at the results part.