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.
Similar content being viewed by others
References
Anh, V. V. (1988). On the Hildreth-Houck estimator for a random coefficient regression model, Austral. J. Statist., 30, 189–195.
Cox, D. R. and Hinkley, D. V. (1974). Theoretical Statistics, Chapman and Hall, London.
Dielman, T. E. (1989). Pooled Cross-sectional and Time Series Data Analysis, Dekker, New York.
Godambe, V. P. (1976). Conditional likelihood and unconditional optimum estimating equations, Biometrika, 63, 277–284.
Godambe, V. P. (1985). The foundations of finite sample estimation in stochastic processes, Biometrika, 72, 419–428.
Hildreth, C. and Houck, J. P. (1968). Some estimators for a linear model with random coefficients, J. Amer. Statist. Assoc., 63, 585–595.
Hyde, J. (1980). Determining an average slope, Biostatistics Casebook (eds. R. G. Miller Jr., B. Efron, B. W. Brown Jr. and L. E. Moses), 171–189, Wiley, New York.
Lindsay, B. G. (1982). Conditional score functions: some optimality results, Biometrika, 69, 503–512.
Mantel, H. J. and Godambe, V. P. (1989). Estimating functions for conditional inference: many nuisance parameter case (submitted for publication).
Rao, C. R. (1984). Linear Statistical Inference and Its Applications, Second ed., Wiley Eastern, New Delhi.
Swamy, P. A. V. B. (1971). Statistical Inference in Random Coefficient Regression Models, Springer, Berlin.
Wu, C. F. J. (1987). Jackknife, bootstrap and other resampling methods in regression analysis, Ann. Statist., 14, 1261–1295.
Author information
Authors and Affiliations
About this article
Cite this article
Ramanathan, T.V., Rajarshi, M.B. Optimal estimation in random coefficient regression models. Ann Inst Stat Math 44, 213–227 (1992). https://doi.org/10.1007/BF00058637
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00058637