Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T07:10:25.486Z Has data issue: false hasContentIssue false
  • English
  • Français

Strong Consistency in Nonlinear Regression

Published online by Cambridge University Press:  11 February 2009

G.D. Richardson  and
B.B. Bhattacharyya
G.D. Richardson
Affiliation:
University of Central Florida
B.B. Bhattacharyya
Affiliation:
North Carolina State University
Get access Rights & Permissions [Opens in a new window]

Abstract

Sufficient conditions are given to ensure the existence of a sequence of strongly consistent estimators of an unknown parameter for a nonlinear regression model. The parameter space includes all separable metric spaces but is not assumed to be compact.

Type
Articles
Information
Econometric Theory , Volume 6 , Issue 4 , December 1990 , pp. 459 - 565
Copyright
Copyright © Cambridge University Press 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bahadur, R.R.Rates of convergence of estimates and test statistics. Annals of Mathematical Statistics 38 (1967): 303–324.CrossRefGoogle Scholar
2.Eastwood, B.J. Confidence interval construction in scmi-nonparametric regression estimation. Doctoral Dissertation, North Carolina State University, 1987.Google Scholar
3.Gallant, A.R.Seemingly unrelated nonlinear regressions. Journal of Econometrics 3 (1975): 35–50.CrossRefGoogle Scholar
4.Geman, S. & Hwang, C.R.. Nonparametric maximum likelihood estimation by the method of sieves. Annals of Statistics 10 (1982): 401–414.CrossRefGoogle Scholar
5.Jennrich, R.I.Asymptotic properties of nonlinear least squares estimators. Annals of Mathematical Statistics 40 (1969): 633–643.CrossRefGoogle Scholar
6.Lai, T.L., Robbins, H., & Wei, C.Z.. Strong consistency of least squares estimates in multiple regression. Proceedings of the National Academy of Sciences USA 75 (1978): 3034–3036.CrossRefGoogle ScholarPubMed
7.Malinvaud, E.The consistency of nonlinear regressions. Annals of Mathematical Statistics 41 (1970): 956–969.CrossRefGoogle Scholar
8.Perlman, M.D.On the strong consistency of approximate maximum likelihood estimates. Proceedings of the Sixth Berkeley Symposium 1 (1972): 263–281.Google Scholar
9.Pfanzagl, K.On the measurability and consistency of minimum contrast estimates. Metrika 14 (1969): 249–272.CrossRefGoogle Scholar
10.Richardson, CD. & Bhattacharyya, B.B.. Consistent estimators in nonlinear regression for a noncompact parameter space. Annals of Statistics 14 (1986): 1591–1596.CrossRefGoogle Scholar
11.Richardson, CD. & Bhattacharyya, B.B.. Consistent L1-estimators in nonlinear regression for a noncompact parameter space. Sankhya 49 (1987): 377–387.Google Scholar
12.Taylor, R.L. Stochastic convergence of weighted sums of random elements in linear spaces. Lecture Notes in Mathematics. Number 672. New York: Springer-Verlag, 1978.Google Scholar
13.Wang, J.-L.Strong consistency of approximate maximum likelihood estimators with applications in nonparametrics. Annals of Statistics 13 (1985): 932–946.CrossRefGoogle Scholar
14.Wu, C.-F.Asymptotic theory of nonlinear least squares estimation. Annals of Statistics 9 (1981): 501–513.CrossRefGoogle Scholar