Consistency of concave regression with an application to current-status data. (English) Zbl 1129.62033
Summary: We consider the problem of nonparametric estimation of a concave regression function \(F\). We show that the supremum distance between the least squares estimator and \(F\) on a compact interval is typically of order \((\log(n)/n)^{2/5}\). This entails rates of convergence for the estimator’s derivative. Moreover, we discuss the impact of additional constraints on \(F\) such as monotonicity and pointwise bounds. Then we apply these results to the analysis of current status data, where the distribution function of the event times is assumed to be concave.
MSC:
62G08 | Nonparametric regression and quantile regression |
62G20 | Asymptotic properties of nonparametric inference |
62G07 | Density estimation |