Reconstruction of a regression line from specifically censored data

Through some misunderstanding the original data cloud was partly obliterated: all the data points above the regression line have been discarded. And also the regression line itself was lost. The question is: can the regression line be reconstructed from the available, censored data and certain information about the original data? We assume that the original data were `neat', that is without outliers and other irregularities, and where the lost regression line (obtained using OLS estimation) fitted them well. In the paper various methods are presented to reconstruct the regression line. Some methods estimate slope and intercept of the regression line simultaneously. Other methods estimate these parameters separately. Some methods are direct, others are iterative. Some methods use statistical tests, others use imputed data. Some methods are non-parametric, others are parametric.

Willenborg, L. (2025). Reconstruction of a regression line from specifically censored data. Discussion paper, Statistics Netherlands, The Hague/Heerlen.