Confidence intervals for the mean of a population containing many zero values under unequal-probability sampling

In many applications a finite population contains a large proportion of zero values that make the population distribution severely skewed An unequal probability sampling plan compounds the problem, and as a result the normal approximation to the distribution of various estimators has poor precision The central-limit theorem based confidence intervals for the population mean are hence unsatisfactory Complex designs also make It hard to pin down useful likelihood functions hence a direct likelihood approach is not an option In this paper we propose a pseudo-likelihood approach The proposed pseudo log likelihood function is an unbiased estimator of the log-likelihood function when the entire population is sampled Simulations have been carried out When the inclusion probabilities are related to the unit values the pseudo likelihood intervals are superior to existing methods in terms of the coverage probability the balance of non-coverage rates on the lower and upper sides and the interval length An application with a data set from the Canadian Labour Force Survey 2000 also shows that the pseudo-likelihood method performs more appropriately than other methods The Canadian Journal of Statistics 38 582-597 2010 (C) 2010 Statistical Society of Canada