Robust estimation and testing in one-way ANOVA for Type II censored samples: skew normal error terms

ABSTRACT

Censoring can be occurred in many statistical analyses in the framework of experimental design. In this study, we estimate the model parameters in one-way ANOVA under Type II censoring. We assume that the distribution of the error terms is Azzalini's skew normal. We use Tiku's modified maximum likelihood (MML) methodology which is a modified version of the well-known maximum likelihood (ML) in the estimation procedure. Unlike ML methodology, MML methodology is non-iterative and gives explicit estimators of the model parameters. We also propose new test statistics based on the proposed estimators. The performances of the proposed estimators and the test statistics based on them are compared with the corresponding normal theory results via Monte Carlo simulation study. A real life data is analysed to show the implementation of the methodology presented in this paper at the end of the study.

Keywords:

• One-way ANOVA
• Type II censoring
• modified likelihood
• skew normal
• efficiency

Disclosure statement

We thank to the editor and the reviewers for their valuable comments and suggestions which greatly improved the paper.