Small area estimation for spatially correlated populations - a comparison of direct and indirect model-based methods

Linear mixed models underpin many small area estimation (SAE) methods. In this paper we investigate SAE based on linear models with spatially correlated small area effects where the neighbourhood structure is described by a contiguity matrix. Such models allow efficient use of spatial auxiliary information in SAE. In particular, we use simulation studies to compare the performances of model-based direct estimation (MBDE) and empirical best linear unbiased prediction (EBLUP) under such models. These simulations are based on theoretically generated populations as well as data obtained from two real populations (the ISTAT farm structure survey in Tuscany and the US Environmental Monitoring and Assessment Program survey). Our empirical results show only marginal gains when spatial dependence between areas is incorporated into the SAE model

Outlier robust small area estimation

Recently proposed outlier robust small area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data. This naturally leads one to consider an outlier robust bias correction for these estimators. We develop this idea, proposing two different analytical mean-squared error estimators for the ensuing bias-corrected outlier robust estimators. Simulations based on realistic outlier-contaminated data show that the bias correction proposed often leads to more efficient estimators. Furthermore, the mean-squared error estimation methods proposed appear to perform well with a variety of outlier robust small area estimators

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Not AvailableIndia is agriculture based country and has experienced an enormous change in food and nutrition utilization design since the financial change in mid 1990s. Agribusiness is considered as the backbone for Indian economy, therefore Indo Gangetic Plain (IGP) holds vast agricultural importance contributing to major portion to our national income. High financial development rates of Indian economy have neglected to enhance food security in India. The welfare of an expanding economy are not shared equally as the country is still home to one-third of the world’s poor. Hunger in India is considered as a genuine imprint on its development and food security has now evolved as a principal issue. Presently, interest in agriculture, nutrition, and dietary security is a prime worry for the country to accomplish the target of encroachment. An expansive area of Indian population is experiencing lack of healthy sustenance and deficiency of nourishment grains. This paper demonstrates nourishment utilization design across selected social and economic groups in the states coming under IGP region of India which includes West Bengal, Bihar, Uttar Pradesh Punjab and Haryana. The analysis helps in distinguishing the disparities among calorie, protein and fat consumption in IGP region. An attempt has also been made in recognizing socio-economic groups suffering from deficiencies in nutrition consumption.Not Availabl

Multipurpose small area estimation

Sample 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/

Small Area Estimation with Skewed Data

In 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

Improved Direct Estimators for Small Areas

Unbiased 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

Outlier robust small area estimation

Recently proposed outlier robust small area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data. This naturally leads down to the idea of an outlier robust bias correction for these estimators. In this paper we develop this idea and also propose two different analytical mean squared error estimators for the ensuring bias corrected outlier robust estimators. Simulations based on realistic outlier contaminated data show that the proposed bias correction often leads to more efficient estimators. Furthermore the proposed mean squared error estimators appear to perform well with a variety of outlier robust smal area estimators

Improved Direct Estimators for Small Areas

Unbiased 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

Estimation of small domain means for zero contaminated skewed data

For skewed data linear model assumptions are questionable. Consequently, the standard techniques for small domain estimation based on linear mixed model can be inefficient. The estimation methods for small domains for skewed data that are linear following a log-log transformation are investigated by Chandra and Chambers (2006). However, application of their methods is limited to strictly positive survey variables. In many surveys (e.g. business and enterprises, income and expenditure, agricultural and ecological surveys etc) variables that are skewed often take zero values. In this paper we introduce small domain estimation techniques for skewed data in presence of zeros. In this context, following Fletcher et at. (2005) and Karlberg (2000) we extend Chandra and Chambers (2006) approach of small domain estimation under a mixture model. Our empirical results show the method works well and produces an efficient set of small area estimates