Performance of Resampling Variance Estimation Techniques with Imputed Survey data.

1
Performance of Resampling Variance Estimation
Techniques with Imputed Survey data.
2

• The Jackknife variance estimation based on
  adjusted imputed values proposed by Rao and Shao
  (1992).
• The Bootstrap procedure proposed by Shao and
  Sitter (1996)

3
Performance

• We carry out a Montecarlo study.
• For each replication, we compute
• Relative bias
• Relative mean square error
• The 95 confidence interval based on the normal
  distribution

4
Imputation methods

• Ratio and mean imputation
• For each method we consider several fractions of
  missing data, with and without covariates

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1 case Structural Business Survey

• Population Annual Industrial Business Survey
  (completely enumerates enterprises with 20 or
  more employees) of size N16,438
• The variable to impute Turnover
• Auxiliary variable total expense

6
2 caseRetail Trade Index Survey

• Population sample of businesses from the Retail
  Trade Index Survey of size N9,414
• The variable to impute Turnover
• Auxiliary variable the same month year ago
  turnover

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1 caseMontecarlo study

• Simple random samples without replacement of
  sizes n100, 500, 1000 and 5000
• Non-response in the turnover variable is randomly
  generated (response mechanism uniform)
• A loss of about 30 is simulated

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2 caseMontecarlo study

• Stratified random samples without replacement of
  sizes n800, 1500, 2200 and 3000
• Non-response in the turnover variable is randomly
  generated (response mechanism uniform)
• Missing data are generated following a
  distribution similar to the true missing value
  pattern observed in the survey.

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Montecarlo study

• Number of replications is 200,000 for each
  auxiliary variable, imputation method and sample
  size

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Results (I)

• The performance of the jackknife variance
  estimator is better for larger sample sizes and
  for ratio imputation.
• The jackknife variance performs poorly. This
  shows that strong skewness and kurtosys of
  imputed variable can influence considerably the
  results.

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Results (II)

• The relative bias is large for small sizes, then
  decreases and increases again when the sampling
  fraction becomes non-negligible
• The coverage rate is not close to the nominal one
  even for large samples. (Due to the skewed and
  heavy-tailed distributions of the variables)

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Conclusions (I)

• Ratio imputation should be used instead of mean
  whenever auxiliary variable are avalaible.
• In these examples, the stratification of the
  sample doesnt improve the quality of the the
  jackknife variance estimator

13
Conclusions (II)

• The percentile bootstrap performs better than the
  jackknife for coverage rate of the confidence
  intervals and the reverse is true for mean square
  errors and bias of the variance.