Purely sequential bounded-risk point estimation of the negative binomial mean under various loss functions: one-sample problem
The paper provides a purely sequential, bounded-risk methodology [\textit{L. J. Willson} and \textit{J. L. Folks}, Commun. Stat., Sequential Anal. 2, 55--70 (1983; Zbl 0594.62095); \textit{S. Zacks}, Stage-wise adaptive designs. Hoboken, NJ: John Wiley \& Sons (2009; Zbl 1171.62065)] to estimate an unknown mean \(\mu\) of the negative binomial distribution under different forms of loss functions. The list of the considered loss functions includes Linex loss (customary and modified) and the squared error loss. The cases of an unknown and known thatch parameter \(\tau\) is handled. It is shown that the proposed approach satisfies the first order asymptotic efficiency and the first-order asymptotic risk efficiency. The proposed methodologies have been checked based on small and moderate sample sizes sets of simulations. The real data from statistical ecology are also treated by these estimation strategies.
scientific article; zbMATH DE number 6943458
scientific article