1,721,016 research outputs found
Small Area Estimation Under Linear and Generalized Linear Mixed Models With Time and Area Effects
No full textThis is the theory component of the report on small area estimation theory that was prepared as part of Southampton’s involvement in the EURAREA “Enhancing small area estimation techniques to meet European Needs” project IST 2000-26290 in the European Union’s Fifth Research And Technological Development Framework Programme
Improved Direct Estimators for Small Areas
No full textUnbiased direct estimators for small area quantities are usually considered too variable to be of any practical use. In this paper we propose a class of model-based direct estimators for small area quantities that appears to overcome this objection, in the sense that these estimators are comparable in efficiency to the indirect model-based small area estimators (e.g. empirical best linear unbiased predictors, or EBLUPs) that are now widely used. There are many practical advantages associated with such model-based direct (MBD) estimators, arising from the fact that they are computed as weighted linear combinations of the actual sample data from the small areas of interest. Note that in this case the weights ‘borrow strength’ via a model that explicitly allows for small area effects. One particular advantage that we explore in this paper is that estimation of mean squared error (MSE) is then straightforward, using well-known methods that are in common use for population level estimates. Empirical results reported in this paper show that the MBD estimator represents a real alternative to the EBLUP, with the simple MSE estimator associated with the MBD estimator providing good coverage performance. We also report results that indicate that the MBD estimator may be more robust than the EBLUP when the small area model is incorrectly specified. Furthermore, the MBD approach is easily extended to provide multi-purpose weights that are efficient across a range of variables, including variables that are unsuitable for EBLUP, e.g. variables that contain a significant proportion of zeros
Multipurpose small area estimation
No full textSample surveys are generally multivariate, in the sense that they measure more than oneresponse variable. In theory, each variable can then be assigned an optimal weight forestimation purposes. However, it is often a distinct practical advantage to have a singleweight that is used with all variables collected in the survey. This paper describes howsuch multipurpose sample weights can be constructed when small area estimates of thesurvey variables are required. The approach is based on the model-based direct (MBD)method of small area estimation described in Chambers and Chandra (2006). Empiricalresults reported in this paper show that MBD estimators for small areas based onmultipurpose weights perform well across a range of variables that are often of interest inbusiness surveys. Furthermore, these results show that the proposed approach is robust tomodel misspecification and also efficient for the variables ill-suited to standard methodsof small area estimation (e.g. variables that contain a significant proportion of zeros).<br/
Out of Sample Estimation for Small Areas using Area Level Data
No full textA Fay-Herriot type model with independent area effects is often assumed when small area estimates based on area level data are required. However, under this approach out of sample areas are limited to synthetic estimates. In this paper we relax the independent area effects assumption, allowing area random effects to be spatially correlated. Empirical best linear unbiased predictors are then developed for areas in sample as well as those that are not in sample, with variance components estimated via maximum likelihood and residual (restricted) maximum likelihood. An expression for the mean cross-product error (MCPE) matrix of the small area estimators is derived, as is an estimator of this matrix. The estimation approach described in the paper is then evaluated by a simulation study, which compares the new method with other methods of small area estimation for this situation
Small Area Estimation with Skewed Data
No full textIn business surveys, data typically are skewed and the standard approach for small area estimation based on linear mixed models lead to inefficient estimates. In this paper, we discuss small area estimation techniques for skewed data that are linear following a suitable transformation. In this context, implementation of the empirical best linear unbiased prediction (EBLUP) approach under transformation to a linear mixed model is complicated. However, this is not the case with the model-based direct (MBD) approach (Chambers and Chandra, 2006), which is based on weighted linear estimators. We extend the MBD approach to skewed data using sample weights derived via model calibration based on a log transform model with random area effects. Our results show this estimator is both efficient and robust with respect to the distribution of these random effects. An application to real data demonstrates the satisfactory performance of the method
Maximum Likelihood with Auxiliary Information
No full textAnalysis of survey data does not happen in a vacuum. We typically know more about the target population than just the data observed in the survey. In some cases this extra information can be incorporated via calibration of survey weights. However, model fitting using weights often leads to increased standard errors. Also, weights are usually calibrated to a relatively small set of variables, while population data may be known for many more variables. Here we use the general approach to maximum likelihood estimation for complex surveys described in Breckling et al. (1994) to develop methods for efficiently incorporating external population information into model fitting using survey data. In particular, we focus on two simple, but very popular, models fitted to survey data. These are the linear regression model and the logistic regression model
Survey Estimation Under Informative Non-Response with Follow-up
No full textThis paper deals with survey estimation when there is partial follow-up of sample non-response. Two different approaches that make use of the follow-up data are presented, the first based on weighting and the other on prediction, with appropriate variance estimators developed for each case. A simulation evaluation of these approaches using synthetic data and informative non-response is then used to contrast them with a basic weighting approach that does not take advantage of the follow-up survey. Our results indicate that the new approaches lead to significant improvement as far as estimation of the population total is concerned
Bias Adjusted Estimation for Small Areas with Outlying Values
No full textSmall area estimation techniques typically rely on regression models that use both covariates and random effects to explain between domain variation. Chambers and Tzavidis (2006) describe a novel approach to small area estimation that is based on modelling quantile-like parameters of the conditional distribution of the target variable given the covariates. This is an outlier robust approach that avoids conventional Gaussian assumptions and the problems associated with specification of random effects, allowing inter-domain differences to be characterized by the variation of area-specific M-quantile coefficients. These authors observed, however, that M-quantile estimates of small area means are biased with the magnitude of the bias being related to the presence of outliers in the data. In this paper we propose a bias adjustment to the M-quantile small area estimator of the mean that is based on representing this estimator as a functional of the small area distribution function. The method is then generalized for estimating other quantiles of the distribution function in a small area. The effect of this bias adjustment on small area estimation with random effects models in the presence of model misspecification is also examined
Empirical Best Linear Unbiased Prediction for Out of Sample Areas
No full textModels for small area estimation based on a random effects specification typically assume population units in different areas are uncorrelated. However, they can be extended to account for the correlation between areas by assuming that area random effects are spatially correlated. In this paper we suggest a simple variance-covariance structure for such a spatial correlation structure within the context of a linear model for the population characteristic of interest, and derive estimates of parameters and components of variance using maximum likelihood and restricted maximum likelihood methods. This allows empirical best linear unbiased predictions for area totals to be computed for areas in sample as well as those that are not in sample. An expression for the mean cross-product error (MCPE) matrix of these predicted small area totals is derived, as is an estimator of this matrix. The estimation approach described in the paper is then evaluated by a simulation study, which compares the new method with other methods of small area estimation for this situation
Small Area Estimation: A Review of Methods Based on the Application of Mixed Models
No full textThis is the review component of the report on small area estimation theory that was prepared as part of Southampton’s involvement in the EURAREA “Enhancing small area estimation techniques to meet European Needs” project IST 2000-26290 in the European Union’s Fifth Research And Technological Development Framework Programme
- …
