Abstract

Conditions of stability and asymptotic normality are derived for solutions of equations of form\(\sum _{k = 1}^n f(\theta , \eta _k , x_k ) = \sum _{k = 1}^n \xi _k\). Heref(θ, ·) is a family of functions and (ξk, ηk) is a sequence of conditionally independent variables inRr given on xk, k≥1, where xk is a sequence with values in an arbitrary space that satisfies a certain ergodicity condition. The continuous-time case is also considered. The asymptotic properties of maximum likelihood estimators and moment method estimators are investigated for observation of weakly dependent variables.

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