Nonparametric estimation for quantile in binary regression models

In this article we propose a new estimator of the quantile function. It is based on nonparametric modified Reed-Muench estimators of a distribution function $F(x)$ in the binary regression models. Conditions for weak consistency and asymptotic normality are given. We compare the new proposal with some existing methods. Those include the double-kernel technique of Yu and Jones (1998), the adjusted version of the Stute (1986), estimator suggested by Borodina (2019) based on the Nadaraya-Watson type estimators. The Comparison is done by asymptotic mean squared error and asymptotic mean. Our methods also have the practical application, for example to quantile estimation to the work Hayes and Mantel (1958). Calculations on these data are made in Tikhov and Shkileva (2019).