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SOME CONVERGENCE THEORY FOR ITERATIVE ESTIMATION PROCEDURES WITH AN APPLICATION TO SEMIPARAMETRIC ESTIMATION

Published online by Cambridge University Press:  19 July 2005

Jeff Dominitz  and
Robert P. Sherman
Jeff Dominitz
Affiliation:
Carnegie Mellon University
Robert P. Sherman
Affiliation:
California Institute of Technology
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Abstract

We develop general conditions for rates of convergence and convergence in distribution of iterative procedures for estimating finite-dimensional parameters. An asymptotic contraction mapping condition is the centerpiece of the theory. We illustrate some of the results by deriving the limiting distribution of a two-stage iterative estimator of regression parameters in a semiparametric binary response model. Simulation results illustrating the computational benefits of the first-stage iterative estimator are also reported.We thank a co-editor and two referees for comments and criticisms that led to significant improvements in this paper. We also thank Roger Klein for providing us with Gauss code to compute his estimator.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 4 , August 2005 , pp. 838 - 863
Copyright
© 2005 Cambridge University Press

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References

REFERENCES

Aliprantis, C.D. & K.C. Border (1994) Infinite Dimensional Analysis. Springer-Verlag.
Bickel, P. (1975) One-step Huber estimates in the linear model. Journal of the American Statistical Association 70, 428–434.Google Scholar
Burden, R.L., J.D. Faires, & A.C. Reynolds (1981) Numerical Analysis. PWS Publishers.
Chamberlain, G. (1986) Asymptotic efficiency in semi-parametric models with censoring. Journal of Econometrics 32, 189–218.Google Scholar
Cosslett, S.R. (1987) Efficiency bounds for distribution-free estimators of the binary choice and censored regression models. Econometrica 55, 559–586.Google Scholar
Dieudonné, J. (1969) Foundations of Modern Analysis. Academic Press.
Heckman, J.J. & B. Honoré (1990) The empirical content of the Roy model. Econometrica 58, 1121–1149.Google Scholar
Horowitz, J. (1992) A smoothed maximum score estimator for the binary response model. Econometrica 60, 505–531.Google Scholar
Ichimura, H. (1997) Asymptotic Distribution of Non-parametric and Semiparametric Estimators with Data Dependent Smoothing Parameters. Manuscript, Department of Economics, University of Pittsburgh.
Klein, R.W. & R.H. Spady (1993) An efficient semiparametric estimator for binary response models. Econometrica 61, 387–421.Google Scholar
Lehmann, E.L. (1983) Theory of Point Estimation. Wiley.
McLachlan, G.J. & T. Krishnan (1997) The EM Algorithm and Extensions. Wiley.
Pakes, A. & D. Pollard (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.Google Scholar
Pastorello, S., V. Patilea, & E. Renault (2003) Iterative and recursive estimation in structural non-adaptive models. Journal of Business & Economic Statistics 21, 449–509.Google Scholar
Robinson, P.M. (1988) The stochastic difference between econometric estimators. Econometrica 56, 531–548.Google Scholar
Sherman, R.P. (1994) U-processes in the analysis of a generalized semiparametric regression estimator. Econometric Theory 10, 372–395.Google Scholar
Wang, W. & M. Zhou (1995) Iterative Least Squares Estimator of Binary Choice Models: A Semiparametric Approach. Working paper, University of Kentucky College of Business and Economics.