Small area statistics are important tools for planning policies in specific regional and administrative areas, as well as for satisfy the general request of information of social and economics conditions in local areas. The so-called spatio-temporal models extend spatial models to time series data. These models strengthen survey direct estimators by considering space-time correlated random-area effects The classic Fay-Herriot model can be extended after including a space-time effect to the standard random-area effect in the regression equation. In most studies, the time-varying effects usually follow an AR(1) process. Otherwise, random walk process, seasonal effects, and more complicated temporal models with random slopes have been studied. In order to consider time correlation in small area estimation, a further approach is based on the state-space models. These models produce estimates at area and time updating the estimates over time by the Kalman filter equations. At the time instant t, the Eblup estimators of the state vector (in these type of models is denominated the model "transition equation"), that define the so--called mesurement equation - i.e., the vector of the model fixed and random effects - are obtained on the basis of the data observed up to time (t-1). The chapter is dedicated to the unit level spatio-temporal models, in the context of the Eblup estimation.
Unit Level Spatio-temporal Models
SALVATORE, Renato
2016-01-01
Abstract
Small area statistics are important tools for planning policies in specific regional and administrative areas, as well as for satisfy the general request of information of social and economics conditions in local areas. The so-called spatio-temporal models extend spatial models to time series data. These models strengthen survey direct estimators by considering space-time correlated random-area effects The classic Fay-Herriot model can be extended after including a space-time effect to the standard random-area effect in the regression equation. In most studies, the time-varying effects usually follow an AR(1) process. Otherwise, random walk process, seasonal effects, and more complicated temporal models with random slopes have been studied. In order to consider time correlation in small area estimation, a further approach is based on the state-space models. These models produce estimates at area and time updating the estimates over time by the Kalman filter equations. At the time instant t, the Eblup estimators of the state vector (in these type of models is denominated the model "transition equation"), that define the so--called mesurement equation - i.e., the vector of the model fixed and random effects - are obtained on the basis of the data observed up to time (t-1). The chapter is dedicated to the unit level spatio-temporal models, in the context of the Eblup estimation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
