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OPTIMAL ESTIMATION IN RANDOM

COEFFICIENT REGRESSION MODELS

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T. V. RAMANATHAN AND M. B. RAJARSHI

*Department of Statistics, University of Poona, Pune, 411 007, India*
(Received May 15, 1990; revised November 22, 1990)

**Abstract.**
In linear regression models with random coefficients, the
score function usually involves unknown nuisance parameters in the form of
weights.
Conditioning with respect to the sufficient statistics for the nuisance
parameter,
when the parameter of interest is held fixed, eliminates the nuisance
parameters and
is expected to give reasonably good estimating functions. The present paper
adopts
this approach to the problem of estimation of average slope in random
coefficient
regression models. Four sampling situations are discussed. Some asymptotic
results
are also obtained for a model where neither the regressors nor the random
regression
coefficients replicate. Simulation studies for normal as well as non-normal
models
show that the performance of the suggested estimating functions is quite
satisfactory.

*Key words and phrases*:
Conditional estimating function, random
coefficient regression models, semi-parametric models, stratified data.

**Source**
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