Moments Asymptotic Expansion of the Least Squares Estimator of the Vector-Parameter of Nonlinear Regression with Correlated Observations

Олександр Володимирович Іванов, Катерина Костянтинівна Москвичова

Abstract


A nonlinear regression model with continuous time and mean square continuous separable measurable Gaussian stationary random noise with zero mean and integrable covariance function is considered. Parameter estimation in the models of such kind is an important problem of statistics of random processes. In this paper, the first terms of asymptotic expansions of the bias vector and covariance matrix of the least square estimator of nonlinear regression function vector parameter are obtained. The machinery of the theory of stochastic processes and asymptotic theory of nonlinear regression were used to derive the results. In particular, the theorems on stochastic expansion of the least square estimator for smooth regression function and on strengthened consistency of the least squares estimator of the nonlinear regression model multidimensional parameter have been used. Obtained results allow answering question important in applications about asymptotic behavior of the first and second moments of the least squares estimator of nonlinear regression model parameter.

Keywords


Nonlinear regression mode; Stationary Gaussian noise; Least squares estimator; Asymptotic expansion

References


A.V. Ivanov and N.N. Leonenko, Statistical Analysis of Random Fields. Dordecht,Boston,London: Kluwer Aca­demic Publishers, 1989, 244 p.

N.N. Leonenko, Limit Theorems for Random Fields with Singular Spectrum. Dordecht, Boston, London: Kluwer Academic Publishers, 1999, 401 p.

A.V. Ivanov and N.N. Leonenko, “Robust Estimators in Non-linear Regression Models with Long-Range Depen­den­ce”, Springer Optimization and its Applications, vol. 28, pp. 193–221, 2009.

Іванов О.В., Савич І.М. Про асимптотичний розподіл оцінки Коенкера–Бассета параметра регресії з силь­но залежним шумом // Укр. мат. журнал. – 2011. – 63, № 8. ­– С. 1030–1052.

A.V. Ivanov et al., “Limit Theorems for weighted nonli­near transformations of Gaussian stationary pro­ces­ses with singular spectra”, The Annals of Probability, vol. 41, no. 2, pp. 1088–1114, 2013.

Ибрагимов И.А., Хасьминский Р.З. Асимптотическая тео­рия оценивания.М.: Наука, Глав. ред. физ.-мат. лит-ры, 1979. – 528 с.

A.V. Ivanov, Asymtotic Theory of Nonlinear Regression. Dordecht,Boston,London: Kluwer Academic Publishers, 1997, 327 p.

G.P.Y. Clarke, “Moments of the Least Squares Estimators in a Nonlinear Regression Model”, J. Roy. Statist. Soc. B, vol. 42, pp. 227–237, 1980.

Гихман И.И., Скороход А.В. Введение в теорию слу­чай­ных процессов. – М.: Наука, 1965. – 656 c.


GOST Style Citations


 

 





DOI: https://doi.org/10.20535/1810-0546.2014.4.28229

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 NTUU KPI