Abstract
We obtain an asymptotic expansion of the functional of the jackknife method, which is used for the estimation of the variance of observational errors in a nonlinear regression model.
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C. C. Frangos, “An updated bibliography on the jackknife method,”Commun. Statist. Theory Meth.,16, 1543–1584 (1987).
C. F. J. Wu, “Jackknifing, bootstrap and other resampling methods in regression analysis (with discussion),”Ann. Statist.,14, No. 4, 1261–1296 (1986).
J. Shao, “Consistency of least-squares estimator and its jackknife variance estimator in nonlinear models,”Can. J. Statist.,20, No. 4, 415–428 (1992).
S. Zwanzig, “A third order asymptotic comparison of least squares jackknifing and cross-validation for error variance estimation in nonlinear regression,”Math. Operationsforsch. Statist.,16, No. 1, 47–54 (1985).
A. V. Ivanov,Theory of Estimation of Parameters of Nonlinear Regression Model [in Russian], Doctor Degree Thesis (Physics and Mathematics), Kiev (1991).
A. V. Ivanov, “Asymptotic expansion for the distribution of least-squares estimator for parameters of nonlinear regression model,”Teor. Ver. Primen.,21, No. 3, 571–584 (1976).
A. V. Ivanov, “Two theorems on consistency of the least-squares estimator,”Teor. Ver. Mat. Statist., No. 28, 25–34 (1983).
T. A. Bardadym and A. V. Ivanov, “Asymptotic expansions associated with the estimation of the variance of observational errors for “signal-plus-noise” model,”Teor. Ver. Mat. Statist., No. 33, 11–20 (1985).
Yu. D. Grigor'ev,Statistical Deduction in Nonlinear Regression Analysis [in Russian], NETI, Novosibirsk (1992).
R. N. Bhattacharia and R. Ranga Rao,Normal Distribution Approximation and Asymptotic Expansions [Russian translation], Nauka, Moscow (1982).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 443–451, April, 1995.
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Bardadym, T.A., Ivanov, A.V. Asymptotic expansions associated with the jackknife functional. I. Ukr Math J 47, 513–523 (1995). https://doi.org/10.1007/BF01056036
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DOI: https://doi.org/10.1007/BF01056036