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SEMIPARAMETRIC RANDOM COEFFICIENT

REGRESSION MODELS

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RUDOLF BERAN

*Department of Statistics, University of California, Berkeley, Berkeley, CA 94720, U.S.A.*
(Received March 23, 1992; revised January 11, 1993)

**Abstract.**
Linear regression models with random coefficients
express the idea that each individual sampled may have a different linear
response function. Technically speaking, random coefficient regression
encompasses a rich variety of submodels. These include deconvolution or
affine-mixture models as well as certain classical linear regression
models that have heteroscedastic errors, or errors-in-variables, or
random effects. This paper studies minimum distance estimates for the
coefficient distributions in a general, semiparametric, random
coefficient regression model. The analysis yields goodness-of-fit tests
for the semiparametric model, prediction regions for future responses,
and confidence regions for the distribution of the random coefficients.

*Key words and phrases*:
Minimum distance, empirical
characteristic function, errors-in-variables, deconvolution, random
effects, statistical inference.

**Source**
( TeX ,
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