### 2002-10

#### A resampling approach for under-estimating a finite population total from a censored sample

Series: 2002-10, Preprints

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

This paper was published in:
Communications in statistics 32 (2003), 12, S.2305-2320.