Weighted L1-estimates for the First-order Bifurcating Autoregressive Model. Issue 8 (13th September 2016)

• Record Type: Journal Article
• Authors: Elbayoumi, Tamer M.; Terpstra, Jeff
• Is Part Of: Communications in statistics. Volume 45:Issue 8(2016)
• Page Start: 2991
• Page End: 3013
• Publication Date: 2016-09-13
• Subjects: Asymptotic theory -- Bifurcating Autoregressive -- Robust -- Weighted L1; 62G08; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2014.938826
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract : We developed robust estimators that minimize a weighted L 1 norm for the first-order bifurcating autoregressive model. When all of the weights are fixed, our estimate is an L 1 estimate that is robust against outlying points in the response space and more efficient than the least squares estimate for heavy-tailed error distributions. When the weights are random and depend on the points in the factor space, the weighted L 1 estimate is robust against outlying points in the factor space. Simulated and artificial examples are presented. The behavior of the proposed estimate is modeled through a Monte Carlo study.