On exact confidence intervals in a competing risks model with generalized hybrid type-I censored exponential data

Abstract

In a recent paper by Mao, Shi and Sun that appeared in Journal of Statistical Computation and Simulation, the authors discuss, among other approaches, the construction of exact confidence intervals for the underlying parameters by ‘pivoting the cumulative distribution functions’ of the corresponding maximum likelihood estimators (MLEs). The authors assume that this method is applicable without providing the appropriate justification. In this short note the two requirements for the applicability of this method are discussed, namely, the stochastic monotonicity of the MLEs and the existence of solutions to the equations defining the exact confidence interval's endpoints.

Keywords:

• competing risks
• exponential distribution
• generalized type-I hybrid censoring
• maximum likelihood estimators
• stochastic monotonicity
• pivoting the CDF

Acknowledgement

The author thank the associate editor and one reviewer for their comments which helped to improve the paper.