Bootstrap for estimating the MSE of the Spatial EBLUP

This work assumes that the small area quantities of interest follow a Fay–Herriot model with spatially correlated random area effects. Under this model, parametric and nonparametric bootstrap procedures are proposed for estimating the mean squared error of the empirical best linear unbiased predictor (EBLUP). A simulation study based on the Italian Agriculture Census 2000 compares bootstrap and analytical estimates of the MSE and studies their robustness to non-normality. Results indicate lower bias for the non-parametric bootstrap under specific departures from normality.

[1]  Domingo Morales,et al.  Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model , 2007, Comput. Stat. Data Anal..

[2]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[3]  Harry H. Kelejian,et al.  A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model , 1999 .

[4]  Sw. Banerjee,et al.  Hierarchical Modeling and Analysis for Spatial Data , 2003 .

[5]  Monica Pratesi,et al.  Small area estimation: the EBLUP estimator based on spatially correlated random area effects , 2008, Stat. Methods Appl..

[6]  Tapabrata Maiti,et al.  On parametric bootstrap methods for small area prediction , 2006 .

[7]  N. Cressie,et al.  Mean squared prediction error in the spatial linear model with estimated covariance parameters , 1992 .

[8]  Jiming Jiang.  REML estimation: asymptotic behavior and related topics , 1996 .

[9]  N. Salvati,et al.  Small area estimation for spatial correlation in watershed erosion assessment , 2006 .

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

[11]  Carl-Erik Särndal,et al.  Model Assisted Survey Sampling , 1997 .

[12]  J. Rao,et al.  On measuring the variability of small area estimators under a basic area level model , 2005 .

[13]  Daniel R. Jeske,et al.  Mean Squared Error of Estimation or Prediction under a General Linear Model , 1992 .

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

[15]  Danny Pfeffermann,et al.  Bootstrap Approximation to Prediction MSE for State–Space Models with Estimated Parameters , 2005 .

[16]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[17]  Malay Ghosh,et al.  Small Area Estimation: An Appraisal , 1994 .

[18]  L. Anselin.  Spatial Econometrics: Methods and Models , 1988 .

[19]  G. K. Shukla,et al.  Spatio-Temporal Models in Small Area Estimation , 2005 .

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

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

[22]  Domingo Morales,et al.  Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model , 2008, Comput. Stat. Data Anal..

[23]  María Dolores Ugarte,et al.  Prediction error estimators in Empirical Bayes disease mapping , 2008 .

[24]  Tapabrata Maiti,et al.  Nonparametric estimation of mean-squared prediction error in nested-error regression models , 2006 .

[25]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[26]  Daniel A. Griffith,et al.  Exploring relationships between semi-variogram and spatial autoregressive models , 1993 .