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VARIANCE ESTIMATION OF MICROSIMULATION MODELS THROUGH SAMPLE REUSE 253 SUMMARY Recent advances in variance estimation and in computational power now make possible the assessment of the variability in microsimulation models. The basic process is to use resampling techniques on the sample survey underlying the model. Application of the bootstrap (or a similar technique), in the manner I have described, would represent an important step forward in assessing the reliability of microsimulation model output. In addition, for any other information about weights or marginal totals, a parametric model should be fit to them so that uncertainty about this information can be taken into account. Finally, if a statistical match or other imputation is used in the model, ideas related to multiple imputation should be used to measure the contribution of the imputation to the overall variability of the results of the microsimulation model. In addition, to understand the variability of a microsimulation model, it is necessary to have a clear idea of what the model is. For example, one should understand what modifications to the data have been made and when and why they are made. It is important to differentiate between the model itself and other versions of the model, and choices that are made within the model. Clearly, the application of these techniques will require some new programming, and it will not be easy until the arrival of the new computing technologies that are expected within the next 5 years. But the benefits of assessing the precision of the estimates from microsimulation models should encourage this effort. REFERENCES Bickel, P., and Freedman, D. 1981 Some asymptotic theory for the bootstrap. Annals of Statistics 9:1196â1217. Diaconis, P., and Efron, B. 1983 Computer-intensive methods in statistics. Scientific American 248:116â130. Efron, B. 1979 Bootstrap methods: Another look at the jackknife. Annals of Statistics 7:1â26. 1981 Nonparametric standard errors and confidence intervals (with discussion). Canadian Journal of Statistics 9:139â172. 1982 The jackknife, the bootstrap, and other resampling plans. SIAM-CBMS-National Science Foundation Monograph No. 38. 1986 Computer-Intensive Methods in Statistical Regression. Technical report #245. Department of Statistics, Stanford University, Palo Alto, Calif. Hampel, F. 1974 The influence curve and its role in robust estimation. Journal of the American Statistical Association 69:383â393. Jaeckel, L. 1972 The Infinitesimal Jackknife. Unpublished memorandum, #MM 72â1215â11. Bell Laboratories, Morristown, N.J.
VARIANCE ESTIMATION OF MICROSIMULATION MODELS THROUGH SAMPLE REUSE 254 Johns, M.V., Jr. 1987 Importance Sampling for Bootstrap Confidence Intervals. Technical report. Department of Statistics, Stanford University, Palo Alto, Calif. Little, R.J.A., and Rubin, D.B. 1987 Statistical Analysis with Missing Data. New York: John Wiley & Sons. McCarthy, P.J. 1969 Pseudo- replication: Half- samples. Review of the International Statistical Institute 37:239â263. Miller, R.G., Jr. 1964 A trustworthy jackknife. Annals of Mathematical Statistics 39:1594â1605. 1974a An unbalanced jackknife. Annals of Statistics 2:80â891. 1974b The jackknifeâA review. Biometrika 61:1â17. Quenouille, M. 1949 Approximate tests of correlation in time- series. Journal of the Royal Statistical Society, Series B 11:68â84. Rao, J.N.K., and Wu, C.F.J. 1988 Resampling inference with complex survey data. Journal of the American Statistical Association 83:231â 241. Rodgers, W.L. 1984 An evaluation of statistical matching. Journal of Business and Economic Statistics 2:91â102. Rubin, D.B. 1986 Statistical matching us ing file concatenation with adjusted weights and multiple imputations. Journal of Business and Economic Statistics 4:86â94. Singh, K. 1981 On the asymptotic accuracy of Efron's bootstrap. Annals of Statistics 9:1187â1195. Stone, M. 1974 Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Series B 36:111â 147. Tibshirani, R. 1985 How Many Bootstrap Replications. Technical report. Department of Statistics, Stanford University. Tukey, J.W. 1958 Bias and confidence in not quite large samples (abstract). Annals of Mathematical Statistics 29:614. Wolfson, M., and Rowe, G. 1990 Biased Divorce: Validation of Marital Status Life Tables and Microsimulation Models. Unpublished technical report. Statistics Canada, Ottawa.