Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling

• Published in: Journal of statistical computation and simulation Vol. 86; no. 15; pp. 3059 - 3067
• Main Author: Muggeo, Vito M. R.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 12-10-2016; Taylor & Francis Ltd
• Subjects: Breakpoint detection; Breast; Computer simulation; Gene expression; Mathematical models; non-standard inference; Nuisance; Patients; piecewise linear; Primary: 62F03; Regression; score test; Secondary: 62J02; Statistical tests; Statistics; threshold value
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2016.1149855

We introduce a score-type statistic to test for a non-zero regression coefficient when the relevant term involves a nuisance parameter present only under the alternative. Despite the non-regularity and complexity of the problem and unlike the previous approaches, the proposed test statistic does not require the nuisance to be estimated. It is simple to implement by relying on the conventional distributions, such as Normal or t, and it justified in the setting of probabilistic coherence. We focus on testing for the existence of a breakpoint in segmented regression, and illustrate the methodology with an analysis on data of DNA copy number aberrations and gene expression profiles from 97 breast cancer patients; moreover some simulations reveal that the proposed test is more powerful than its competitors previously discussed in literature.