Bootstrap adjustments of signed scoring rule root statistics. Issue 4 (21st April 2018)

• Record Type: Journal Article
• Authors: Mameli, V.; Musio, M.; Ventura, L.
• Is Part Of: Communications in statistics. Volume 47:Issue 4(2018)
• Page Start: 1204
• Page End: 1215
• Publication Date: 2018-04-21
• Subjects: Asymptotic expansions -- Higher-order inference -- Parametric bootstrap -- Regression models -- Robustness -- Tsallis scoring rule; Primary 62F05, 62F40 -- Secondary 62H10, 62F35; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2017.1309427
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: Scoring rules give rise to methods for statistical inference and are useful tools to achieve robustness or reduce computations. Scoring rule inference is generally performed through first-order approximations to the distribution of the scoring rule estimator or of the ratio-type statistic. In order to improve the accuracy of first-order methods even in simple models, we propose bootstrap adjustments of signed scoring rule root statistics for a scalar parameter of interest in presence of nuisance parameters. The method relies on the parametric bootstrap approach that avoids onerous calculations specific of analytical adjustments. Numerical examples illustrate the accuracy of the proposed method.