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IPS280 Erniel B. Barrios et al.
over per capita income should be done after obtaining the annual estimate of
the income per household to ensure that the per capita income decile to which
sampled household belong to its true income decile.

Provincial Estimates for Median Income (Bootstrap Sampling)
In computing for the annualized model-assisted estimates, both the
estimate and the variance are needed. Using the conventional method of
obtaining the median estimate, generation of annualized model-assisted
estimate for the median is not possible since generation of the variance of
median is computationally intensive. As a solution, bootstrap resampling was
done. Bootstrap resampling allows the computation of the standard error and
the coefficient of variation for the estimates of the median. It also minimizes
the bias and improves the reliability of estimates (Mooney and Duval, 1993)
for the estimates over per capita income decile. Aside from computing the
bootstrap estimates for the median, the bootstrap estimates for the
annualized overall income and expenditure and design-based mean income
over per capita income decile were also obtained. The purpose of obtaining
the estimates for the overall income and expenditure is to verify robustness of
the bootstrap estimation procedure. The expected value for the overall income
and expenditure is that its annualized bootstrap estimates were close to the
original annualized model-assisted estimates.

4. Concluding notes
Aggregated model-assisted annualized estimates for provinces in partially
rotated samples coincide with design-unbiased estimates at the domains
(regions). The CVs at the national and regional level for the overall income and
expenditure as well as CVs at the national and regional level for income and
expenditure over income class were all less than 10%. Moreover, provincial
estimates by different disaggregation groups also yield reliable estimates.
From simulation studies, increasing the percentage of matched samples does
not necessarily affect improve efficiency of the estimates, but CV decreases
with increasing matched sample size. Meanwhile for the estimate per capita
income decile, it is recommended that the sample be selected with
stratification per income class or income decile. On the estimation of median
family income by per capita income decile, bootstrap method is
recommended. It is proposed to use the rotated sample to produce reliable
provincial estimates while retaining the sample size of the Family Income and
Expenditure Survey.

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