Estimation of the first and second order parameters in regression models with special structure (Q1193985)

The author considers variance components models \(Y=X\beta+\varepsilon\), \(E\varepsilon =0\), \(E\varepsilon\varepsilon'=\sum^ S_{i=1}\theta_ iV_ i\). Examples in which such models appear are mentioned: gravimetric networks, geodetic networks, experiments checking the stability of dams, atomic stations, etc. The number of observations and/or the number of parameters are then often very large. Dividing the parameters in necessary and nuisance parameters, \(y\) is transformed to \(Ty\) which is independent of nuisance parameters. MINQE-theory (local theory) is studied in the transformed model. Special attention is devoted to replication models and multistage structures (the regression matrix is blocktriangular).