rsae-package

Robust Small Area Estimation

The package implements methods to fit the basic unit-level model (also known as model type "B" in Rao, 2003, or nested-error regression model in Battese et al., 1988), to predict area-specific means by the empirical best linear unbiased predictor (EBLUP) or a robust prediction method (Copt and Victoria-Feser, 2009; Heritier et al., 2011), and to compute the mean square prediction error of the predicted area-level means by a parametric bootstrap (Sinha and Rao, 2009; see also Hall and Maiti, 2006; Lahiri, 2003).

The methods are discussed in Schoch (2012). package

Details

Implemented methods

• maximum likelihood estimator

• Huber-type M-estimator (RML II of Richardson and Welsh, 1995, not the method proposed in Sinha and Rao, 2009); see Schoch (2012) for details

How to

Data analysis involves the following steps:

1. prepare the data/ specify the model for estimation; see saemodel()
2. fit the model by various (robust) methods; see fitsaemodel()
3. (robustly) predict the random effects and the area means; see robpredict()

References

Battese, G. E., Harter, R. M., and W.A. Fuller (1988). An error component model for prediction of county crop areas using. Journal of the American Statistical Association 83 , 28--36. tools:::Rd_expr_doi("https://doi.org/10.2307/2288915")

Copt, S. and M.-P. Victoria-Feser (2009). Robust Predictions in Mixed Linear Models, Research Report, University of Geneva.

Lahiri, P. (2003). On the impact of bootstrap in survey sampling and small area estimation. Statistical Science 18 , 199--210. tools:::Rd_expr_doi("https://doi.org/10.1214/ss/1063994975")

Hall, P. and T. Maiti (2006). On parametric bootstrap methods for small area prediction. Journal of the Royal Statistical Society. Series B 68 , 221--238. tools:::Rd_expr_doi("https://doi.org/10.1111/j.1467-9868.2006.00541.x")

Heritier, S., Cantoni, E., Copt, S., and M.-P. Victoria-Feser (2009). Robust methods in Biostatistics, New York: John Wiley and Sons.

Rao, J.N.K. (2003). Small Area Estimation, New York: John Wiley and Sons.

Richardson, A.M. and A.H. Welsh (1995). Robust restricted maximum likelihood in mixed linear model. Biometrics 51 , 1429--1439. tools:::Rd_expr_doi("https://doi.org/10.2307/2533273")

Schoch, T. (2012). Robust Unit-Level Small Area Estimation: A Fast Algorithm for Large Datasets. Austrian Journal of Statistics 41 , 243--265. tools:::Rd_expr_doi("https://doi.org/10.17713/ajs.v41i4.1548")

Sinha, S.K. and J.N.K. Rao (2009). Robust small area estimation. Canadian Journal of Statistics 37 , 381--399. tools:::Rd_expr_doi("https://doi.org/10.1002/cjs.10029")