×

Asymptotic properties of estimators in semiparametric regression models with random censorship. (Chinese. English summary) Zbl 1174.62378

Summary: The semiparametric regression model \(Y_i=x_i\beta+g(t_i)+\sigma_i\varepsilon_i,\;i=1,2,\cdots,n\), is considered where \(\sigma^2_i=f(u_i)\). When \(Y_i\) is randomly censored to the right because of certain disturbances, in the situation that the censored distribution function is unknown, estimators of the parameter \(\beta\) and regression function \(g(t)\) are constructed based on censored observations. Under appropriate conditions, it is proved that the estimator \(\widehat{\beta}_n\) is asymptotically normal and that \(\widehat{g}_n(t)\) has optimal convergence rate.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
PDFBibTeX XMLCite