Performance of Resampling Variance Estimation Techniques with Imputed Survey data.

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

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

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

1 case: Structural Business Survey Population : Annual Industrial Business Survey (completely enumerates enterprises with 20 or more employees) of size N=16,438 The variable to impute: Turnover Auxiliary variable: total expense

2 case:Retail Trade Index Survey Population : sample of businesses from the Retail Trade Index Survey of size N=9,414 The variable to impute: Turnover Auxiliary variable: the same month year ago turnover

1 case:Montecarlo study Simple random samples without replacement of sizes n=100, 500, 1000 and 5000 Non-response in the turnover variable is randomly generated (response mechanism uniform) A loss of about 30% is simulated

2 case:Montecarlo study Stratified random samples without replacement of sizes n=800, 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.

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

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.

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)

Conclusions (I) Ratio imputation should be used instead of mean whenever auxiliary variable are avalaible. In these examples, the stratification of the sample doesn’t improve the quality of the the jackknife variance estimator

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.