A robust sequential fixed-width confidence interval for count data based on Bhattacharyya-Hellinger distance estimator. Issue 1 (2nd January 2016) - Sriram, T. N.; Samadi, S. Y.
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.