A robust sequential fixed-width confidence interval for count data based on Bhattacharyya-Hellinger distance estimator. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Sriram, T. N.; Samadi, S. Yaser
• Is Part Of: Sequential analysis. Volume 35:Issue 1(2016)
• Page Start: 84
• Page End: 107
• Publication Date: 2016-01-02
• Subjects: Asymptotic consistency -- asymptotic efficiency -- fixed-width confidence interval -- gross-error contamination -- maximum likelihood -- minimum Hellinger distance -- robustness -- stopping rule; 62L10 -- 62G20 -- 62G35; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2016.1132061
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: For count data having an unknown mass function g 0, we use the minimum Bhattacharyya-Hellinger distance (MBHD) estimator and a stopping rule to construct a sequential fixed-width confidence interval for a functional T ( g 0 ) = θ0, where f θ0 is the best-fitting parametric model achieving the MBHD between g 0 and any member of a parametric class of mass functions. We establish the asymptotic consistency and efficiency properties of the sequential confidence interval and the expected sample size, respectively, as the half-width d → 0. When the count data come from a gross-error contamination model g α, L = (1 − α) f θ + αδ{ L } for α ∈ (0, 1), where a parametric model f θ is mixed with a point mass δ{ L } located at a value L, we reparameterize L = L d such that L d → ∞ as d → 0 and theoretically show that the expected sample size is affected by α, whereas the coverage probability of the sequential confidence interval depends on the rate of [ T ( g α, L d ) − θ]/ d, as d → 0. Our reparameterization fully exploits the MBHD estimator's inherent ability to progressively ignore increasing values of L, providing an asymptotically consistent sequential fixed-width interval estimator of θ. When f θ is Poisson (θ), simulations are conducted to corroborate our theoretical results and to contrast the performance of the MBHD with that of the maximum likelihood estimator (MLE) of θ. A real data on Death Notice, modeled as a negative binomial, are analyzed to compare and contrast the performance of our sequential MBHD procedure with that of the MLE.