Empirical likelihood confidence intervals for adaptive cluster sampling

Adaptive cluster sampling (ACS) is an efficient sampling design for estimating parameters of rare and clustered populations. It is widely used in ecological research. The modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators based on small samples under ACS have often highly skewed distributions. In such situations, confidence intervals based on traditional normal approximation can lead to unsatisfactory results, with poor coverage properties. Christman and Pontius (Biometrics 56:503–510, 2000) showed that bootstrap percentile methods are appropriate for constructing confidence intervals from the HH estimator. But Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) showed that bootstrap confidence intervals from the HT estimator are even worse than the normal approximation confidence intervals. In this article, we consider two pseudo empirical likelihood functions under the ACS design. One leads to the HH estimator and the other leads to a HT type estimator known as the Hájek estimator. Based on these two empirical likelihood functions, we derive confidence intervals for the population mean. Using a simulation study, we show that the confidence intervals obtained from the first EL function perform as good as the bootstrap confidence intervals from the HH estimator but the confidence intervals obtained from the second EL function perform much better than the bootstrap confidence intervals from the HT estimator, in terms of coverage rate.     

Green technology for sustainable surface protection of steel from corrosion: a review

Plants contain substances that inhibit corrosion. Here we review biomass-based corrosion inhibitors from plant leaves, nuts, and fruit peels, after treatment with acids, bases or saline solutions. The mechanism of corrosion inhibition involves a monolayer coverage, according to isotherm and Langmuir models. Plant extract-based corrosion inhibitors contain heteroatoms whose electrons pair in the p-electron level in multiple bonds and the vacant d-orbitals of iron. Corrosion inhibition under marine conditions involves various chemical interactions between metals and dissolved ionic components.