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ESTIMATION OF CHARACTERISTICS FROM RESTRICTED
OR "CENSORED" SAMPLE DATA
w. A. Hendricks
H. F. Huddleston
Research and Development Staff
Agricultural Estimates Division
Agricultural Marketing Service
u.s. Departm~nt of Agriculture
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ESTIMATION OF CHARACTERISTICS FROM RESTRICTED
OR "CENSORED" SAMPLE DATA
1. Introduction
A restricted estimator from a random" sample may be viewed as a special type,
of partial coverage, in which all cases above a specified size "criterion
are omitted. The technique is essentially one of estimation from incom-
plete data using either a "truncated" or "censored" sample. However, the
technique proposed is an alternative to using the complete data for skewed
distributions.
While the estimated sample characteristics for the complete
data is properly assessed by the sampling errors, the apriori knowledge of
the distribution other than the coefficient of variation (in setting sample
size) is not used.
In some cases this is due to the fact that individual
units cannot be placed in size strata, or due to the lack of control which
can be exercised over individual characteristics in a multi-purpose survey.
The extreme upper tail of the sample distribution is censored in favor of
the expected value (or a maximum likelihood value) where the inclusion of
the extreme values are expected to make the variance unduly large and in
all likelihood increase the mean.
The establishment of censored points at specified levels based on a
negligible portion of the upper tail (m < .02) has proven useful in sur-
veys.
In those situations where all tHe sampling units with extr¢mely
large values of the characteristic cannot be identified in advance and
sampled with certainty, a relatively few sampling-units may exert,con-
siderable influence on the mean and the variance.
The device described
appears promising where the type of distribution is known in advartce.
The procedure has been applied to Type III distributions with coefficient
of variations of 100 to 200 percent.
It is also contem