Disaggregation of spatial autoregressive processes

An aggregated Gaussian random field, possibly strong-dependent, is obtained from accumulation of i.i.d. short memory fields via an unknown mixing density φφ which is to be estimated. The so-called disaggregation problem is considered, i.e. φφ is estimated from a sample of the limiting aggregated field while samples of the elementary processes remain unobserved. Estimation of the density is via its expansion in terms of orthogonal Gegenbauer polynomials. After defining the estimators, their consistency and convergence rates are discussed. An example of application to ββ-convergence in EU GDP per capita is discussed.