Improved approximate confidence intervals for censored data

Abstract

<p>This dissertation includes three papers. The first paper compares different procedures to compute confidence intervals for parameters and quantiles of the Weibull distribution for Type I censored data. The methods can be classified into three groups. The first group contains methods based on the commonly-used normal approximation for the distribution of (possibly transformed) studentized maximum likelihood estimators. The second group contains methods based on the likelihood ratio statistic and its modifications. The methods in the third group use a parametric bootstrap approach, including the use of bootstrap-type simulation to calibrate the procedures in the first two groups. We use the Monte Carlo simulation to investigate the finite sample properties of these procedures. Exceptional cases, which are due to problems caused by the Type I censoring, are noted;The second paper extends the results from Jensen (1993) and show that the distribution of signed squared root likelihood ratio statistics can be approximated by its bootstrap distribution up to second order accuracy when data are censored. Similar results apply to likelihood ratio Statistics and Probability; Our simulation study based on Type I censored data and the two parameter Weibull model shows that the bootstrap signed square root likelihood ratio statistics and its modification outperform the other methods like bootstrap-t and BCa in constructing one-sided confidence bounds;The third paper describes existing methods and develops new methods for constructing simultaneous confidence bands for a cumulative distribution function (cdf). Our results are built on extensions of previous work by Cheng and Iles (1983, 1988). A general approach is presented for construction of two-sided simultaneous confidence band for a continuous parametric model cdf from complete and censored data using standard large-sample approximations and then extending and comparing these to corresponding simulation or bootstrap calibrated versions of the same methods. Both two-sided and one-sided simultaneous confidence bands for location-scale parameter model are discussed in detail including situations with complete and censored data. A simulation for the Weibull distribution and Type I censored data is given. We illustrate the implementation of the methods with an application to estimate probability of detection (POD) used to assess nondestructive evaluation (NDE) capability.</p>