On the Impact of Bootstrap in Survey Sampling and Small-Area Estimation

Development of valid bootstrap procedures has been a challenging problem for survey samplers for the last two decades. This is due to the fact that in surveys we constantly face various complex issues such as complex correlation structure induced by the survey design, weighting, imputation, small-area estimation, among others. In this paper, we critically review various bootstrap methods developed to deal with these challenging issues. We discuss two applications where the bootstrap has been found to be effective.

[1]  J. Booth,et al.  Standard Errors of Prediction in Generalized Linear Mixed Models , 1998 .

[2]  Hiroshi Saigo,et al.  A Repeated Half­Sample Bootstrap and Balanced Repeated Replications for Randomly Imputed Data , 2001 .

[3]  B. Efron Better Bootstrap Confidence Intervals , 1987 .

[4]  J. Rao Small Area Estimation , 2003 .

[5]  P J McCarthy,et al.  The bootstrap and finite population sampling. , 1985, Vital and health statistics. Series 2, Data evaluation and methods research.

[6]  R. Little Survey Nonresponse Adjustments for Estimates of Means , 1986 .

[7]  R J Carroll,et al.  On meta-analytic assessment of surrogate outcomes. , 2000, Biostatistics.

[8]  Jiming Jiang,et al.  A unified jackknife theory for empirical best prediction with M-estimation , 2002 .

[9]  D. Rubin INFERENCE AND MISSING DATA , 1975 .

[10]  J. Rao On Variance Estimation with Imputed Survey Data , 1996 .

[11]  G. Kalton,et al.  The treatment of missing survey data , 1986 .

[12]  Rachel M. Harter,et al.  An Error-Components Model for Prediction of County Crop Areas Using Survey and Satellite Data , 1988 .

[13]  P. Lahiri,et al.  A UNIFIED MEASURE OF UNCERTAINTY OF ESTIMATED BEST LINEAR UNBIASED PREDICTORS IN SMALL AREA ESTIMATION PROBLEMS , 2000 .

[14]  D. Pfeffermann Small Area Estimation‐New Developments and Directions , 2002 .

[15]  K F Rust,et al.  Variance estimation for complex surveys using replication techniques , 1996, Statistical methods in medical research.

[16]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[17]  R. Sitter A resampling procedure for complex survey data , 1992 .

[18]  J. N. K. Rao,et al.  Some recent advances in model-based small area estimation , 1999 .

[19]  Fan Zhang,et al.  Variance Estimation of Imputed Survey Data. Working Paper Series. , 1998 .

[20]  D. Rubin,et al.  Multiple Imputation for Interval Estimation from Simple Random Samples with Ignorable Nonresponse , 1986 .

[21]  Bradley Efron,et al.  Missing Data, Imputation, and the Bootstrap , 1994 .

[22]  J. Shao,et al.  The jackknife and bootstrap , 1996 .

[23]  Vipin Arora,et al.  Empirical Bayes Estimation of Finite Population Means from Complex Surveys , 1997 .

[24]  Bradley Efron,et al.  Missing Data, Imputation, and the Bootstrap: Rejoinder , 1994 .

[25]  B. Efron Bootstrap Methods: Another Look at the Jackknife , 1979 .

[26]  R. Little Pattern-Mixture Models for Multivariate Incomplete Data , 1993 .

[27]  D. Freedman,et al.  Asymptotic Normality and the Bootstrap in Stratified Sampling , 1984 .

[28]  Bradley P. Carlin,et al.  A Sample Reuse Method for Accurate Parametric Empirical Bayes Confidence Intervals , 1991 .

[29]  Tapabrata Maiti,et al.  Empirical Bayes Estimation of Relative Risks in Disease Mapping , 2002 .

[30]  D. Rubin Formalizing Subjective Notions about the Effect of Nonrespondents in Sample Surveys , 1977 .

[31]  C. Morris Parametric Empirical Bayes Inference: Theory and Applications , 1983 .

[32]  R. N. Kackar,et al.  Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models , 1984 .

[33]  D. Rubin Multiple imputation for nonresponse in surveys , 1989 .

[34]  J. Rao,et al.  The estimation of the mean squared error of small-area estimators , 1990 .

[35]  Randy R. Sitter,et al.  Comparing three bootstrap methods for survey data , 1992 .

[36]  J. Shao,et al.  Bootstrap for Imputed Survey Data , 1996 .

[37]  C. F. Wu,et al.  Resampling Inference with Complex Survey Data , 1988 .

[38]  R. Fay,et al.  Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data , 1979 .

[39]  Morris H. Hansen,et al.  Sample survey methods and theory , 1955 .

[40]  P. Lahiri,et al.  On measures of uncertainty of empirical Bayes small-area estimators , 2003 .

[41]  Ferry Butar Butar Empirical Bayes methods in survey sampling , 1997 .

[42]  J. N. K. Rao,et al.  Bootstrap and other methods to measure errors in survey estimates , 1988 .