Comparisons of approximate confidence intervals for the smallest extreme value distribution simple linear regression model under time censoring

Abstract

Exact confidence interval estimation for accelerated life regression models with censored smallest extreme value (or Weibull) data is often impractical. This paper evaluates the accuracy of approximate confidence intervals based on the asymptotic normality of the maximum likelihood estimator, the asymptotic X²distribution of the likelihood ratio statistic, mean and variance correction to the likelihood ratio statistic, and the so-called Bartlett correction to the likelihood ratio statistic. The Monte Carlo evaluations under various degrees of time censoring show that uncorrected likelihood ratio intervals are very accurate in situations with heavy censoring. The benefits of mean and variance correction to the likelihood ratio statistic are only realized with light or no censoring. Bartlett correction tends to result in conservative intervals. Intervals based on the asymptotic normality of maximum likelihood estimators are anticonservative and should be used with much caution.

Keywords:

• Accelerated life testing
• Bartlett correction
• likelihood ratio statistic
• mean and variance correction
• Weibull