Nonparametric Estimation of the Slope of a Truncated Regression

A nonparametric estimate ,B* is presented for the slope of a regression line Y = 83oX + V subject to the truncation Y c yo. This model is relevant to a cosmological controversy which concerns Hubble's Law in Astronomy. The estimate /3 * corresponds to the zero-crossing of a random function S, (/3), which for each /8 is a Mann-Whitney type of statistic designed to measure heterogeneity among the calculated residuals Y /3X. The asymptotic distribution of P * is derived making extensive use of U-statistics to show that Sn (/3o) is asymptotically normal and then showing that S,, (/3) behaves like Sn (/3o) plus a deterministic term which is locally linear. Results on asymptotic efficiency are compared with finite sample size results by simulation.