Abstract
In a nonlinear regression model there has been obtained an asymptotic expansion of the distribution function of the least squares estimate of the dispersion of the observation error. There have been found two first terms of the asymptotic expansion.
Literature cited
S. A. Zwanzig, “A third order asymptotic comparison of least squares, jacknifing and cross-validation for error variance estimation in nonlinear regression,” Math. Operationforsch, und Statist. Ser. Statist.,16, 47–54 (1985).
W. A. Schmidt and S. A. Zwanzig, “Second order asymptotics in nonlinear regression,” J. Multivar. Anal.,18, 187–215 (1986).
M. B. Qumsiyeh, Edgeworth Expansion in Regression Models, Theses Ph. D. Dissertation, Indiana University and Bethlehem University (1988).
A. V. Ivanov, “Asymptotic expansion for the distribution of the least squares estimate of a parameter of a nonlinear regression function,” Teor. Veroyatn. Ee Primen.,21, No. 3, 571–583 (1976).
A. V. Ivanov and N. N. Leonenko, Statistical Analysis of Random Fields, Vishcha Shkola, Kiev (1986).
T. A. Bardadym and A. V. Ivanov, “Asymptotic expansions, related to an estimate of the dispersion of the observation error, for ‘signal plus noise’ models,” Teor. Veroyatn. Mat. Statist.,33, No. 3, 11–20 (1985).
R. N. Bhattacharya and R. Ranga Rao, Normal Approximation and Asymptotic Expansions, Wiley, New York (1976).
S. M. Sadikova, “Some inequalities for characteristic functions,” Teor. Veroyatn. Ee Primen.,11, No. 3, 500–506 (1966).
V. V. Yurinskii, “Estimates for characteristic functions of some degenerate multivariate distributions,” Teor. Veroyatn. Ee Primen.,17, No. 1, 99–110 (1972).
R. N. Bhattacharya, “Refinements of the multidimensional central limit theorem and applications,” Ann. Probab.,5, 1–27 (1977).
J. Pfonzage, “Asymptotically optimum estimation and test procedures,” Proc. Prague Symp. Asymptotic Stat.,1, 201–272 (1973).
R. Michel, “An asymptotic expansion for the distribution of asymptotic maximum likelihood estimators of vector parameters,” J. Multivar. Anal.,15, 67–82 (1975).
T. W. Anderson, An Introduction to Multivariate Stochastic Analysis, Wiley, New York (1958) [2nd ed. (1984)].
R. N. Bhattacharya and J. K. Gosh, “On the validity of the formal Edgeworth expansion,” Ann. Statist.,8, No. 2, 434–451 (1978).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 697–703, May, 1991.
Rights and permissions
About this article
Cite this article
Ivanitskaya, L.S., Ivanov, A.V. Asymptotic expansion for the distribution of the dispersion of the observation error in a nonlinear regression model. Ukr Math J 43, 648–655 (1991). https://doi.org/10.1007/BF01058554
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058554