文档介绍：Chapter 6
NON-LINEAR REGRESSION MODELS
TAKESHI AMEMIYA*
Stanford University
Contents
1. Introduction 334
2. Single equation-. case 336
. Model 336
. Asymptotic properties 337
. Computation 341
. Tests of hypotheses 347
. Confidence regions 352
3. Single equation-non-. case 354
3. I. Autocorrelated errors 354
. Heteroscedastic errors 358
4. Multivariate models 359
5. Simultaneous equations models 362
. Non-linear two-stage least squares estimator 362
. Other single equation estimators 370
. Non-linear simultaneous equations 375
. Non-linear three-stage least squares estimator 376
. Non-linear full information maximum likelihood estimator 379
References 385
*This work was supported by National Science Foundation Grant SE%7912965 at the Institute for
Mathematical Studies in the Social Sciences, Stanford University. The author is indebted to the
following people for ments: R. C. Fair, A. R. Gallant, Z. Griliches, M. D. Intriligator,
T. E. MaCurdy, J. L. Powell, R. E. Quandt, N. E. Savin, and H. White.
Handbook of Econometrics, Volume I, Edited by Z. Griliches and . Intriligator
0 North-Holland pany, 1983
334 T. Amemiya
1. Introduction
This is a survey of non-linear regression models, with an emphasis on the theory
of estimation and hypothesis testing rather putation and applications,
although there will be some discussion of the last two topics. For a general
discussion putation the reader is referred to Chapter 12 of this Handbook
by Quandt. My aim is to present the gist of major results; therefore, I will
sometimes omit proofs and less significant assumptions. For those, the reader
must consult the original sources.
The advent of puter technology has made it possible for the
econometrician to estimate an increasing number of non-linear regression models
in recent years. Non-linearity arises in many diverse ways in econometric appli