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M-quantile models with application to poverty mapping 总被引:1,自引:0,他引:1
Nikos Tzavidis Nicola Salvati Monica Pratesi Ray Chambers 《Statistical Methods and Applications》2008,17(3):393-411
Over the last decade there has been growing demand for estimates of population characteristics at small area level. Unfortunately,
cost constraints in the design of sample surveys lead to small sample sizes within these areas and as a result direct estimation,
using only the survey data, is inappropriate since it yields estimates with unacceptable levels of precision. Small area models
are designed to tackle the small sample size problem. The most popular class of models for small area estimation is random
effects models that include random area effects to account for between area variations. However, such models also depend on
strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow
for outlier robust inference. An alternative approach to small area estimation that is based on the use of M-quantile models
was recently proposed by Chambers and Tzavidis (Biometrika 93(2):255–268, 2006) and Tzavidis and Chambers (Robust prediction
of small area means and distributions. Working paper, 2007). Unlike traditional random effects models, M-quantile models do
not depend on strong distributional assumption and automatically provide outlier robust inference. In this paper we illustrate
for the first time how M-quantile models can be practically employed for deriving small area estimates of poverty and inequality.
The methodology we propose improves the traditional poverty mapping methods in the following ways: (a) it enables the estimation
of the distribution function of the study variable within the small area of interest both under an M-quantile and a random
effects model, (b) it provides analytical, instead of empirical, estimation of the mean squared error of the M-quantile small
area mean estimates and (c) it employs a robust to outliers estimation method. The methodology is applied to data from the
2002 Living Standards Measurement Survey (LSMS) in Albania for estimating (a) district level estimates of the incidence of
poverty in Albania, (b) district level inequality measures and (c) the distribution function of household per-capita consumption
expenditure in each district. Small area estimates of poverty and inequality show that the poorest Albanian districts are
in the mountainous regions (north and north east) with the wealthiest districts, which are also linked with high levels of
inequality, in the coastal (south west) and southern part of country. We discuss the practical advantages of our methodology
and note the consistency of our results with results from previous studies. We further demonstrate the usefulness of the M-quantile
estimation framework through design-based simulations based on two realistic survey data sets containing small area information
and show that the M-quantile approach may be preferable when the aim is to estimate the small area distribution function. 相似文献
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Small area estimation: the EBLUP estimator based on spatially correlated random area effects 总被引:1,自引:0,他引:1
This paper deals with small area indirect estimators under area level random effect models when only area level data are available
and the random effects are correlated. The performance of the Spatial Empirical Best Linear Unbiased Predictor (SEBLUP) is
explored with a Monte Carlo simulation study on lattice data and it is applied to the results of the sample survey on Life
Conditions in Tuscany (Italy). The mean squared error (MSE) problem is discussed illustrating the MSE estimator in comparison
with the MSE of the empirical sampling distribution of SEBLUP estimator. A clear tendency in our empirical findings is that
the introduction of spatially correlated random area effects reduce both the variance and the bias of the EBLUP estimator.
Despite some residual bias, the coverage rate of our confidence intervals comes close to a nominal 95%. 相似文献
3.
Roberto Benedetti Monica Pratesi Nicola Salvati 《Statistical Methods and Applications》2013,22(1):81-95
Small area estimators are often based on linear mixed models under the assumption that relationships among variables are stationary across the area of interest (Fay–Herriot models). This hypothesis is patently violated when the population is divided into heterogeneous latent subgroups. In this paper we propose a local Fay–Herriot model assisted by a Simulated Annealing algorithm to identify the latent subgroups of small areas. The value minimized through the Simulated Annealing algorithm is the sum of the estimated mean squared error (MSE) of the small area estimates. The technique is employed for small area estimates of erosion on agricultural land within the Rathbun Lake Watershed (IA, USA). The results are promising and show that introducing local stationarity in a small area model may lead to useful improvements in the performance of the estimators. 相似文献
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Social Indicators Research - The objective of this study is to investigate whether the quality of educational services and the university’s institutional image influence students’... 相似文献
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