02-10
A resampling approach for under-estimating a finite population total from a censored sample
Preprint series: 02-10, Preprints
The paper is published: Communications in statistics 32 (2003), 12, S.2305-2320.
- MSC:
- 62G09 Resampling methods
- 62G15 Tolerance and confidence regions
Abstract: Suppose a finite population of $N$ objects each of which has an unknown value $\mu_i\ge0$, $i=1,\ldots,N$, of a nonnegative characteristic of interest. A random sample has been drawn, but only for a selected subset of the sample the $\mu$-values have been observed. The subset selection procedure has been somewhat obscure, and thus the subsample is censorized rather than random. Despite that, a reliable lower bound for the population total (the sum of all $\mu_i$) is required which uses the statistical information contained in the data. We propose a resampling procedure to construct an under-estimate of the population total. We also consider the case when the objects of the population have unequal sampling probabilities, in particular when the population is divided into a few number of strata with constant probabilities within each stratum. A real data example illustrates the method.
Keywords: Resampling, finite population total, lower confidence bound
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