A nonparametric estimate $\beta^\ast$ is presented for the slope of a regression line $Y = \beta_0X + V$ subject to the truncation $Y \leq y_0$. This model is relevant to a cosmological controversy which concerns Hubble's Law in Astronomy. The estimate $\beta^\ast$ corresponds to the zero-crossing of a random function $S_n(\beta)$, which for each $\beta$ is a Mann-Whitney type of statistic designed to measure heterogeneity among the calculated residuals $Y - \beta X$. The asymptotic distribution of $\beta^\ast$ is derived making extensive use of $U$-statistics to show that $S_n(\beta_0)$ is asymptotically normal and then showing that $S_n(\beta)$ behaves like $S_n(\beta_0)$ plus a deterministic term which is locally linear. Results on asymptotic efficiency are compared with finite sample size results by simulation.
@article{1176346157,
author = {Bhattacharya, P. K. and Chernoff, Herman and Yang, S. S.},
title = {Nonparametric Estimation of the Slope of a Truncated Regression},
journal = {Ann. Statist.},
volume = {11},
number = {1},
year = {1983},
pages = { 505-514},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346157}
}
Bhattacharya, P. K.; Chernoff, Herman; Yang, S. S. Nonparametric Estimation of the Slope of a Truncated Regression. Ann. Statist., Tome 11 (1983) no. 1, pp. 505-514. http://gdmltest.u-ga.fr/item/1176346157/