Asymptotics for robust MOSUM
Linear relations, containing measurement errors in input and output data, are taken into account in this paper. Parameters of these so-called errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of the input-output disturbances. Such an estimate is highly non-linear. Moreover in some realistic situations, the errors cannot be considered as independent by nature. Weakly dependent (- and -mixing) disturbances, which are not necessarily stationary nor identically...
We consider the asymptotic distribution of covariate values in the quantile regression basic solution under weak assumptions. A diagnostic procedure for assessing homogeneity of the conditional densities is also proposed.