Point and interval estimation for extreme-value regression model under Type-II censoring

Inference for the extreme-value regression model under Type-II censoring is discussed. The likelihood function and the score functions of the unknown parameters are presented. The asymptotic variance-covariance matrix is derived through the inverse of the expected Fisher information matrix. Since the maximum likelihood estimators (MLE) cannot be solved analytically, an approximation to these MLE are proposed. The variance-covariance matrix of these approximate estimators is also derived. Next, confidence intervals are proposed based on the MLE and the approximate estimators. An extensive simulation study is carried out in order to study the bias and variance of all these estimators. We also examine the coverage probabilities as well as the expected widths of the confidence intervals. Finally, all the inferential procedures discussed here are illustrated with practical data.