Least absolute deviations estimation for the censored regression model (Q1061446)

This paper deals with the model \(Y_ t=\max (0\), \(x'_ t\beta_ 0+u_ t)\), \(t=1,...,T\). \(u_ t\) are unobservable disturbance terms with median zero and continuous distribution, mutually independent. Then \(\max(0,x'_ t\beta_ 0)\) is the median of \(y_ t\), given the exogenous variables \(x_ t\). \(\beta_ 0\) is estimated by minimizing \(\sum^{T}_{t=1}| y_ t-\max (0,x'_ t\beta)|\) over a compact set B. The author formulates conditions on \(\{x_ t\}\) and \(\{u_ t\}\) in order that the estimators \({\hat \beta}_ T\) of \(\beta\) converge to \(\beta_ 0\) almost surely as \(T\to \infty\). Also conditions are formulated that \(\sqrt{T}({\hat\beta}_ T-\beta_ 0)\) is asymptotically normally distributed. The asymptotic covariance matrix is determined and estimated consistently.