Multiply robust imputation procedures for zero-inflated distributions in surveys
Tóm tắt
Item nonresponse in surveys is usually treated by some form of single imputation. In practice, the survey variable subject to missing values may exhibit a large number of zero-valued observations. In this paper, we propose multiply robust imputation procedures for treating this type of variable. Our procedures may be based on multiple imputation models and/or multiple nonresponse models. An imputation procedure is said to be multiply robust if the resulting estimator is consistent when all models but one are misspecified. The variance of the imputed estimators is estimated through a generalized jackknife variance estimation procedure. Results from a simulation study suggest that the proposed procedures perform well in terms of bias, efficiency and coverage rate.
Tài liệu tham khảo
Berger, Y.G.: A jackknife variance estimator for unistage stratified samples with unequal probabilities. Biometrika 94, 953–964 (2007)
Chan, K.C.G., Yam, S.C.P.: Oracle, multiple robust and multipurpose calibration in missing response problem. Stat. Sci. 29, 380–386 (2014)
Chen, S., Haziza, D.: Multiply robust imputation procedures for the treatment of item nonresponse in surveys. Biometrika 102, 439–453 (2017)
Chen, S., Haziza, D.: Jackknife empirical likelihood method for multiply robust estimation with missing data. Comput. Stat. Data Anal. (2017) (in revision)
Chen, S., Haziza, D.: Multiply robust nonparametric multiple imputation for the treatment of missing data. Stat. Sin. (2017) (in revision)
Duan, X., Yin, G.: Ensemble approaches to estimating the population mean with missing response. Scand. J. Stat. (2017). doi:10.1111/sjos.12281
Fay, R.E.: A design-based perspective on missing data variance. In: Proceedings of the 1991 Annual Research Conference, US Bureau of the Census, pp. 429–440 (1991)
Gelein, B.: Preserving the distribution function in surveys in case of imputation for zero inflated data (2016) (manuscript)
Hájek, J.: Asymptotic theory of rejective sampling with varying probabilities from a finite population. Ann. Inst. Stat. Math. 35, 1491–1523 (1964)
Hájek, J.: Comment on “An essay on the logical foundations of survey sampling” by Basu, D. In: Godambe, V.P., Sprott, D.A. (eds.) Foundations of Statistical Inference, p. 236. Holt, Rinehart, and Winston, Toronto (1971)
Han, P., Wang, L.: Estimation with missing data: beyond double robustness. Biometrika 100, 417–430 (2013)
Han, P.: A further study of the multiply robust estimator in missing data analysis. J. Stat. Plan. Inference 148, 101–110 (2014)
Han, P.: Multiply robust estimation in regression analysis with missing data. J. Am. Stat. Assoc. 109, 1159–1173 (2014)
Haziza, D.: Imputation and inference in the presence of missing data. In: Pfeffermann, D., Rao, C.R. (eds.) Handbook of Statistics. Sample Surveys: Theory Methods and Inference, vol. 29A, pp. 215–246. Elsevier, Amsterdam (2009)
Haziza, D., Rao, J.N.K.: A nonresponse model approach to inference under imputation for missing survey data. Surv. Methodol. 32, 53–64 (2006)
Haziza, D., Nambeu, C.O., Chauvet, G.: Doubly robust imputation procedures for finite population means in the presence of a large number of zeros. Can. J. Stat. 42, 650–669 (2014)
Kang, J.D.Y., Schafer, J.L.: Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data (with discussion). Stat. Sci. 22, 523–539 (2007)
Kim, J.K., Haziza, D.: Doubly robust inference with missing data in survey sampling. Stat. Sin. 24, 375–394 (2014)
Kim, J.K., Park, H.: Imputation using response probability. Can. J. Stat. 34, 171–182 (2006)
Kim, J.K., Rao, J.N.K.: Unified approach to linearization variance estimation from survey data after imputation for item nonresponse. Biometrika 96, 917–932 (2009)
Kim, J.K., Shao, J.: Statistical Methods for Handling Incomplete Data. Chapman and Hall/CRC, London (2013)
Little, R.J.A., Rubin, D.B.: Statistical Analysis with Missing Data, 2nd edn. Wiley, Hoboken (2002)
Ohlsson, E.: Sequential Poisson sampling. J. Off. Stat. 14, 149–162 (1998)
Rao, J.N.K.: On two simple schemas of unequal probability sampling without replacement. J. Indian Stat. Assoc. 3, 173–180 (1965)
Rao, J.N.K., Shao, J.: Jackknife variance estimation with survey data under hot-deck imputation. Biometrika 79, 811–822 (1992)
Rubin, D.B.: Inference and missing data. Biometrika 63, 581–592 (1976)
Sampford, M.R.: On sampling without replacement with unequal probabilities of selection. Biometrika 54, 499–513 (1967)
Shao, J., Sitter, R.R.: Bootstrap for imputed survey data. J. Am. Stat. Assoc. 93, 819–831 (1996)
Shao, J., Steel, P.: Variance estimation for survey data with composite imputation and nonnegligible sampling fractions. J. Am. Stat. Assoc. 94, 254–265 (1999)
Tillé, Y.: Sampling Algorithms. Springer, New York (2006)