For a simple regression model, the problem of estimating the intercept after a preliminary test on the regression coefficient is considered here. Some nonparametric procedures for this problem are formulated and their various asymptotic properties studied. Comparison with the conventional estimation procedures (for both the situations where the regression coefficient is treated as a nuisance parameter or not) has also been made.
"Nonparametric Estimation of Location Parameter After a Preliminary Test on Regression." Ann. Statist. 6 (1) 154 - 168, January, 1978. https://doi.org/10.1214/aos/1176344074