A confidence interval for the slope of a truncated regression (Q580846)

\textit{P. K. Bhattacharya, H. Chernoff} and \textit{S. S. Yang} [Ann. Stat. 11, 505-514 (1983; Zbl 0522.62031)] proposed a nonparametric estimate for the slope of a regression line \(Y=\beta _ 0X+V\) subjected to the truncation \(Y\leq y_ 0\). The estimate corresponds to the zero-crossing of a random function \(S_ n(\beta).\) In this paper an estimate for the asymptotic variance of the estimate of the slope is proposed and the rate of convergence is given. The proofs rest heavily on the local behavior of \(S_ n(\beta)\) in the neighborhood of the true value \(\beta _ 0\).