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2017•Unpublished venueRequires access

Local asymptotic normality for a class of discretely observed nonlinear stochastic systems with unknown perturbation parameter

Xiu Kan, Huisheng Shu

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Abstract

In this paper, the asymptotic properties are addressed for a class of discretely observed nonlinear nonhomogeneous stochastic system with unknown parameter. The local asymptotic normality is derived based on the discrete observation of the approximate maximum likelihood estimator of the unknown parameter in the drift term. The purpose of the addressed problem is to analyze the weak convergence of the likelihood ratio random field, based on which the asymptotic behavior of the likelihood ratio is shown.

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What this paper is about

In this paper, the asymptotic properties are addressed for a class of discretely observed nonlinear nonhomogeneous stochastic system with unknown parameter. The local asymptotic normality is derived based on the discrete observation of the approximate maximum likelihood estimator of the unknown parameter in the drift term. The purpose of the addressed problem is to analyze the weak convergence of the likelihood ratio random field, based on which the asymptotic behavior of the likelihood ratio is shown.

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Available abstract

In this paper, the asymptotic properties are addressed for a class of discretely observed nonlinear nonhomogeneous stochastic system with unknown parameter. The local asymptotic normality is derived based on the discrete observation of the approximate maximum likelihood estimator of the unknown parameter in the drift term. The purpose of the addressed problem is to analyze the weak convergence of the likelihood ratio random field, based on which the asymptotic behavior of the likelihood ratio is shown.

Key concepts: Local asymptotic normality, Asymptotic distribution, Estimator, Mathematics, Nonlinear system, Applied mathematics, Perturbation (astronomy), Estimation theory

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