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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

Abstract

A nonparametric estimate β is presented for the slope of a regression line Y=β0X+V subject to the truncation Yy0. This model is relevant to a cosmological controversy which concerns Hubble's Law in Astronomy. The estimate β corresponds to the zero-crossing of a random function Sn(β), which for each β is a Mann-Whitney type of statistic designed to measure heterogeneity among the calculated residuals YβX. The asymptotic distribution of β is derived making extensive use of U-statistics to show that Sn(β0) is asymptotically normal and then showing that Sn(β) behaves like Sn(β0) plus a deterministic term which is locally linear. Results on asymptotic efficiency are compared with finite sample size results by simulation.

Citation

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

Information

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

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

Subjects:
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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