Bootstrap for estimating the mean squared error 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 EBLUP (Empirical Best Linear Unbiased Predictor). A simulation study compares the bootstrap estimates with an asymptotic analytical approximation and studies the robustness to non-normality. Finally, two applications with real data are described

Bootstrap for estimating the mean squared error 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 EBLUP (Empirical Best Linear Unbiased Predictor). A simulation study compares the bootstrap estimates with an asymptotic analytical approximation and studies the robustness to non-normality. Finally, two applications with real data are described.

Small area models for analysing job placement survey data of the STELLA consortium

Job placement is a very important issue in nowadays governance of universities and data on career of graduates in the labour market are crucial also for evaluating the performance of the courses of study. The University of Pisa is member of the STELLA consortium whose aim is to perform periodic sample and census surveys for investigating and monitoring the career of graduates on the labor market. In this paper the level of satisfaction for the coherence of the employment condition with the studies of graduates one year after the degree is analysed. Small Area Models (SAE) are used to obtain more accurate estimates for the unplanned domains defined by the course of study. Focus is on the Economics and Statistics master's of science or single-cycle degree courses of the University of Brescia and Pisa

Local Comparisons of Small Area Estimates of Poverty: An Application Within the Tuscany Region in Italy

The aim of this paper is to highlight some key issues and challenges in the analysis of poverty at the local level using survey data. In the last years there was a worldwide increase in the demand for poverty and living conditions estimates at the local level, since these quantities can help in planning local policies aimed at decreasing poverty and social exclusion. In many countries various sample surveys on income and living conditions are currently conducted, but their sample size is not enough to obtain reliable estimates at local level. When this happens, small area estimation (SAE) methods can be used. In this paper, a SAE model is used to compute the mean household equivalised income and the head count ratio for the 57 Labor Local Systems of the Tuscany region in Italy for the year 2011. The caveats of the analysis of poverty at the local level using small area methods are many, and some are still not so well explored in the literature, starting from the definition of the target indicators to the relevant dimensions of their measurement. We suggest in this paper that together with the universally recognized multidimensional, longitudinal and local dimensions of poverty, a new dimension must be considered: the price dimension, which should take into account local purchasing power parities to cor- rectly compare the poverty indicators based on income measures

The use of Twitter data to improve small area estimates of households’ share of food consumption expenditure in Italy

The use of big data in many socio-economic studies has received a growing interest in the last few years. In this work we use emotional data coming from Twitter as auxiliary variable in a small area model to estimate Italian households’ share of food consumption expenditure (the proportion of food consumption expenditure on the total consumption expenditure) at provincial level. We show that the use of Twitter data has a potential in predicting our target variable. Moreover, the use of these data as auxiliary variable in the small area working model reduces the estimated mean squared error in comparison with what obtained by the same working model without the Twitter data

Spatial network sampling in small area estimation

The spatial distribution of a population represents an important in sampling designs where that use the network of the contiguities between units as auxiliary information in the frame. Its use is increased in the last decades as the GIS and GPS technologies made more and more cheap to add information regarding the exact or estimated position for each record in the frame. These data may represent a source of auxiliaries that can be helpful to design effective sampling strategies, which, assuming that the observed phenomenon is related with the spatial features of the population, could gather a considerable gain in their efficiency by a proper use of this particular information. This assumption is particularly relevant if we are dealing with not planned geographical domains or, in other terms, if we want that the design will be efficient for a future use within a small area estimation context. A method for selecting samples from a spatial finite population that are well spread over the population in every dimension should guarantee that the variability of the expected sampling ratio should be smaller than that obtained by using a simple random sampling. Some algorithms of sample selection are presented such that a set of units with higher within distance will be selected with higher probability than a set of nearby units. Some examples on real data show that the RMSE of the EBLUP estimates applied to samples selected with these network methods are lower than those obtained by using a classical solution as the Generalized Random Tessellation Stratified (GRTS). The proposed algorithm, even if in its nature it is computationally intensive, seems to be a feasible solution even when dealing with frames relevant to large finite network populations

Poverty Indicators at Local Level: Definitions, Comparisons in Real Terms and Small Area Estimation Methods

The importance of computing poverty measures at sub-national level is nowadays widely attested. Local poverty indicators are relevant both for a detailed planning of the policy actions against poverty and social exclusion, and for the citizens to evaluate their effects. However, there are still open problems to compute adequate sub-national poverty indicators. They refer to: 1) the definition of poverty lines; 2) the methods for accounting the spatial variation of the cost of living to make comparisons in ‘real terms’ between different areas; 3) the use of Small Area Estimation methods when the sample size is not enough to obtain accurate estimates of the indicators at local level. In this paper, we discuss the issues above by presenting some analyses on the impact of using different poverty lines on the value of the poverty rate for the 20 Italian Regions, which represent a planned domain of study in Italy. Then, we estimate the poverty rate for the 110 Italian Provinces, unplanned domains in Italy, by using specific parametric models and SAE methods. The key results highlight strong differences in the territorial distribution of the poverty rate by using national versus sub-national specific poverty lines. The effect of the heterogeneity of the general spatial price indexes on the poverty rates seems instead less important in comparison with the relevant territorial differences in the cost of housing. Moreover, the different methods of estimation of poverty rates at local level provides interesting first results and indicates the route for further research to improve the methods of estimation of poverty at the sub-regional level

Does uncertainty in single indicators affect the reliability of composite indexes? An application to the measurement of environmental performances of Italian regions

In recent decades, the measurement and evaluation of important social and natural phenomena has significantly evolved, with many traditional measurements based on single variables increasingly being replaced by multi- dimensional approaches. One key aspect of these approaches is the development of composite indexes, usually real-value functions of multiple achievements of a group of units. The achievements in each of the selected dimensions are generally synthesised through one or more variables, often referred to as indicators. When in- dicators are obtained through an estimation process, it is crucial to understand if and how their estimation error – for example, sampling error – affects the resulting composite index. This paper presents a methodology based on a parametric bootstrap technique that evaluates to what extent uncertainty in indicators affects the reliability of the aggregate composite index. The method is applied to four composite indexes measuring the environmental performances of Italian regions based on real population and survey data. To our knowledge, this is the first attempt to measure the impact of indicators’ sampling error on composite indexes. If adequately generalised, our methodology could be used in the presence of measurement errors, non- response issues, or other kinds of non-sampling errors