Model checks for two-sample location-scale

Abstract

Two-sample location-scale refers to a model that permits a pair of standardised random variables to have a common base distribution. Function-based hypothesis testing in these models refers to formal tests based on distributions functions, or direct transformations thereof, that would help decide whether or not two samples come from some location-scale family of distributions. For uncensored data, an approach of testing based on plug-in empirical likelihood (PEL) is carried out with sample means and standard deviations as the plug-ins. The method extends to censored data, where censoring adjusted moment estimators provide the requisite plug-ins. The large sample null distribution of the PEL statistic is derived. Since it is not distribution free, a two-sample location-scale appropriate resampling is employed to obtain thresholds needed for the testing. Numerical studies are carried out to investigate the performance of the proposed method. Real examples are presented for both the uncensored and censored cases.

Keywords:

• Gaussian process
• Kaplan–Meier integral
• lagrange multiplier
• likelihood ratio
• survival function

Mathematics Subject Classifications:

• 62G10
• 62N03
• 62N01

Acknowledgments

We sincerely thank the Editor, an Associate Editor, and two reviewers for their valuable inputs that resulted in the final version.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

1. Smoker data available at https://onlinelibrary.wiley.com/doi/10.1002/bimj.201900057

2. Repository name: Mendeley Data. Data identification number: 10.17632/25yjwbphn4.1 Direct URL to data: https://data.mendeley.com/datasets/25yjwbphn4/1

3. Burn data available in R package ‘KMSurv’ under the name burn.