Emilia Rocco

Small area estimation for semicontinuous skewed spatial data: An application to the grape wine production in Tuscany

Linear-mixed models are frequently used to obtain model-based estimators in small area estimation (SAE) problems. Such models, however, are not suitable when the target variable exhibits a point mass at zero, a highly skewed distribution of the nonzero values and a strong spatial structure. In this paper, a SAE approach for dealing with such variables is suggested. We propose a two-part random effects SAE model that includes a correlation structure on the area random effects that appears in the two parts and incorporates a bivariate smooth function of the geographical coordinates of units. To account for the skewness of the distribution of the positive values of the response variable, a Gamma model is adopted. To fit the model, to get small area estimates and to evaluate their precision, a hierarchical Bayesian approach is used. The study is motivated by a real SAE problem. We focus on estimation of the per-farm average grape wine production in Tuscany, at subregional level, using the Farm Structure Survey data. Results from this real data application and those obtained by a model-based simulation experiment show a satisfactory performance of the suggested SAE approach.

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data.

The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to show the practical benefits of the unequal allocation in estimating simultaneously the means of more skewed variables through real data. In particular, the allocation rule suggested in the literature for a single skewed distribution may be easily applied when more than one skewed variable are of interest and an auxiliary variable correlated with them is available. This method can lead to substantial gains in precision for all the study variables with respect to the simple random sampling, and to the balanced ranked set sampling too.

Modelling the location decisions of manufacturing firms with a spatial point process approach

The paper is devoted to explore how the increasing availability of spatial micro-data, jointly with the diffusion of GIS software, allows to exploit micro-econometric methods based on stochastic spatial point processes in order to understand the factors that may influence the location decisions of new firms. By using the knowledge of the geographical coordinates of the newborn firms, their spatial distribution is treated as a realization of an inhomogeneous marked point process in the continuous space and the effect of spatial-varying factors on the location decisions is evaluated by parametrically modelling the intensity of the process. The study is motivated by the real issue of analysing the birth process of small and medium manufacturing firms in Tuscany, an Italian region, and it shows that the location choices of the new Tuscan firms is influenced on the one hand by the availability of infrastructures and the level of accessibility, and on the other by the presence and the characteristics of the existing firms. Moreover, the effect of these factors varies with the size and the level of technology of the new firms. Besides the specific Tuscan result, the study shows the potentiality of the described micro-econometric approach for the analysis of the spatial dynamics of firms.

A Bayesian semiparametric model for non negative semicontinuous data

ABSTRACT When the target variable exhibits a semicontinuous behavior (a point mass in a single value and a continuous distribution elsewhere), parametric “two-part models” have been extensively used and investigated. The applications have mainly been related to non negative variables with a point mass in zero (zero-inflated data). In this article, a semiparametric Bayesian two-part model for dealing with such variables is proposed. The model allows a semiparametric expression for the two parts of the model by using Dirichlet processes. A motivating example, based on grape wine production in Tuscany (an Italian region), is used to show the capabilities of the model. Finally, two simulation experiments evaluate the model. Results show a satisfactory performance of the suggested approach for modeling and predicting semicontinuous data when parametric assumptions are not reasonable.

Estimates for geographical domains through geoadditive models in presence of incomplete geographical information

The paper deals with the matter of producing geographical domains estimates for a variable with a spatial pattern in presence of incomplete information about the population units location. The spatial distribution of the study variable and its eventual relations with other covariates are modeled by a geoadditive regression. The use of such a model to produce model-based estimates for some geographical domains requires all the population units to be referenced at point locations, however typically the spatial coordinates are known only for the sampled units. An approach to treat the lack of geographical information for non-sampled units is suggested: it is proposed to impose a distribution on the spatial locations inside each domain. This is realized through a hierarchical Bayesian formulation of the geoadditive model in which a prior distribution on the spatial coordinates is defined. The performance of the proposed imputation approach is evaluated through various Markov Chain Monte Carlo experiments implemented under different scenarios.

Kernel-Type Smoothing Methods of Adjusting for Unit Nonresponse in Presence of Multiple and Different Type Covariates

This paper deals with the nonresponse problem in the estimation of the mean of a finite population following a nonparametric approach. Weighting adjustment is a popular method for handling unit nonresponse. It operates by increasing the sampling weights of the respondents in the sample using estimates of their respond probabilities. Typically, these estimates are obtained by fitting parametric models relating response occurrences and auxiliary variables. An alternative solution is the nonparametric estimation of the response probabilities. The aim of this paper is to investigate, via simulation experiments, the small-sample properties of kernel regression estimation of the response probabilities when the auxiliary information consists in a mix of continuous and discrete variables. Furthermore the practical behavior of the method is evaluated on data of a web survey on accommodation facilities in the province of Florence.

Two-step centre sampling for estimating the size, total and mean of elusive population

Abstract.The estimation of the size of an elusive population is a frequently addressed problem in many fields of applications. The paper proposes a two step sampling strategy for the estimation of the population size, under the assumption that each unit of the population is present at least in one centre of aggregation. In the first step a sample of centres is selected and in the second step, from the selected centres, a sample of ultimate units is observed. The design extends the traditional network sampling introducing an additional step of selection. The properties of the Horvitz-Thompson type estimator are evaluated in a design-based approach: the estimator is admissible and consistent; the design is measurable. The approach is also used to estimate other descriptive parameters (the total and the mean of a study variable) for the same population. The expressions of the variance of all the proposed estimators and of their unbiased sample estimators are also proposed. The strategy is applied to a simulated population.

A Two-Part Geoadditive Small Area Model for Geographical Domain Estimation

We are interested in estimating small domain means of a response variable that shows a spatial trend and has a continuous skewed distribution with a large number of values clustered at zero. This kind of variable can occur in many surveys, like business or agricultural surveys: examples are the quantity of crops produced or the amount of land allocated for their production collected by the Farm Structure Survey driven by the Italian Statistical Institute. The small sample size within the areas requires the use of small area model dependent methods to increase the effective area sample size by using census and administrative auxiliary data. To account simultaneously for the excess of zeros, the skewness of the distribution and the possible spatial trend of the data, we present a two-part geoadditive small area model. An application to the estimation of the per-farm average grapevine production in Tuscany at Agrarian Region level shows the satisfactory performance of the model.

Spatially-balanced adaptive web sampling

The paper deals with sampling from a finite population that is distributed over space and has a highly uneven spatial distribution. It suggests a sampling design that allocates a portion of the sample units that are well spread over the population and sequentially selects the remaining units in sub-areas that appear to be of more interest according to the study variable values observed during the survey. In order to estimate the population mean while using this sampling design, a computationally intense estimator, obtained via the Rao–Blackwell approach, is proposed and a resampling method is used that makes the inference computationally feasible. The whole sampling strategy is evaluated through several Monte Carlo experiments.

Statistical Characterization of the Virtual Water Trade Network

The water that is used in the production process of a product (a supply, commodity or service) is called the “virtual water” contained in the product. If one country (or region, company, individual, etc.) exports a water intensive product to another country, it exports water in virtual form. Virtual water trade as both a policy instrument and practical means to balance the local, national and global water budget has received much attention in recent years. Several studies have been conducted by researchers from various disciplines including engineers, economists and demographers. The aim of this paper is to improve the statistical characterization of the virtual water flow networks by suggesting a statistical modeling approach for examining their stochastic properties.