A semi-parametric censored regression estimator
In a censored regression model \(y_ i=X^ T_ i \beta +\epsilon_ i\), if \(\epsilon_ i>-X^ T_ i \beta\), \(i=1,...,N\), and \(y_ i=0\), otherwise, the \(\epsilon_ i\) are assumed to be i.i.d., absolutely continuous, \(E(\epsilon_ i)=0\), \(E(\epsilon^ 2_ i)=\sigma^ 2\). Their (unknown) density is approximated by splines (piecewise polynomials) with mesh size approaching 0 as \(N\to \infty\). A quasi maximum likelihood estimation method is applied to the whole set of parameters (usual unknown parameters and values of the density of \(\epsilon\) at the knots of the sieve). Strong consistency of parameter estimates is proved. Since a complete asymptotic distribution theory is unavailable, the performance of the method is presented on simulated data (comparison of various point estimates and bootstrapped confidence intervals).
quasi maximum likelihood estimation method
Strong consistency of parameter estimates
scientific article; zbMATH DE number 3976128
scientific article