Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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. https://doi.org/10.1214/aos/1176346157

Information

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

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

Subjects:
Primary: 62G05
Secondary: 62J05, 85A40

Rights: Copyright © 1983 Institute of Mathematical Statistics

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.11 • No. 2 • June, 1983
Back to Top