The Annals of Statistics

Minimum Distance Estimation in Random Coefficient Regression Models

R. Beran and P. W. Millar

Full-text: Open access

Abstract

Random coefficient regression models are important in modeling heteroscedastic multivariate linear regression in econometrics. The analysis of panel data is one example. In statistics, the random and mixed effects models of ANOVA, deconvolution models and affine mixture models are all special cases of random coefficient regression. Some inferential problems, such as constructing prediction regions for the modeled response, require a good nonparametric estimator of the unknown coefficient distribution. This paper introduces and studies a consistent nonparametric minimum distance method for estimating the coefficient distribution. Our estimator translates the difficult problem of estimating an inverse Radon transform into a minimization problem.

Article information

Source
Ann. Statist., Volume 22, Number 4 (1994), 1976-1992.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325767

Digital Object Identifier
doi:10.1214/aos/1176325767

Mathematical Reviews number (MathSciNet)
MR1329178

Zentralblatt MATH identifier
0828.62031

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62J05: Linear regression

Keywords
Radon transform prediction interval distribution estimate weak convergence metric characteristic function nonparametric semiparametric

Citation

Beran, R.; Millar, P. W. Minimum Distance Estimation in Random Coefficient Regression Models. Ann. Statist. 22 (1994), no. 4, 1976--1992. doi:10.1214/aos/1176325767. https://projecteuclid.org/euclid.aos/1176325767


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