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June, 1983 Nonparametric Estimation of the Slope of a Truncated Regression
P. K. Bhattacharya, Herman Chernoff, S. S. Yang
Ann. Statist. 11(2): 505-514 (June, 1983). DOI: 10.1214/aos/1176346157


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.


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P. K. Bhattacharya. Herman Chernoff. S. S. Yang. "Nonparametric Estimation of the Slope of a Truncated Regression." Ann. Statist. 11 (2) 505 - 514, June, 1983.


Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0522.62031
MathSciNet: MR696063
Digital Object Identifier: 10.1214/aos/1176346157

Primary: 62G05
Secondary: 62J05 , 85A40

Keywords: $U$-statistics , chronometric theory , cosmology , efficiency , Hubble's Law , nonparametric , simulation , truncated regression

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 2 • June, 1983
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