6. Concluding remarks
Jae Kwang Kim and Shu Yang
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We have proposed a fractional hot deck
imputation method that uses a parametric model for
when
contains continuous components.
The proposed method provides robust estimation for the parameters in the sense
that the imputation model is not necessarily equal to the data-generating
model. The price we pay in the FHDI is the loss of efficiency in point
estimation. Under our first simulation, the FHDI estimator for
has the second largest variance
but the smallest mean squared error when the working model is not true, as
compared with other estimators.
The loss of efficiency mainly comes from the
fact that the fractional weights are more variable than those under the PFI
method because some of
are not useful in imputing
That is, the value of
can be very small. The fractional
hot deck imputation under a small imputation size (e.g.
) does not increase the variance
significantly, as can be seen in Table 5.1 under model A.
The proposed fractional imputation method can
actually be used to develop a single imputation method by applying FHDI with
which selects an imputed value
with probability proportional to the fractional weight for each missing unit.
In this case, the FHDI can be used to develop a single imputation that is still
robust against model misspecification. However, weighting calibration cannot
co-exist with single imputation. Calibration constraints can still be achieved
by employing the balanced imputation method as discussed in Chauvet, Deville
and Haziza (2011) or the rejective Poisson sampling of Fuller (2009). Further
investigation along this direction will be a topic of future research.
Acknowledgements
We thank two anonymous referees and the associate editor for
very helpful comments. This research was partially supported by a grant from
NSF (MMS-121339) and by the Cooperative Agreement between the USDA Natural
Resources Conservation Service and the Center for Survey Statistics and
Methodology at Iowa State University.
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