The Annals of Statistics

Minimum Distance Estimation in Random Coefficient Regression Models

R. Beran and P. W. Millar

Full-text: Open access


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

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

First available in Project Euclid: 11 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

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


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.

Export citation