Abstract:

A kernel-type estimator of the quantile function Q(p)=inf{t:F(t)≥p}, 0≤p≤1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.

Key words: Truncated data, Product-limits quantilefunction, kernel estimator, Bahadur representation