Estimation in autoregressive model with measurement error

2011/05/06 by Dedecker, Jérôme, Samson, Adeline, Taupin, Marie-Luce
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1105.1310

Abstract

Consider an autoregressive model with measurement error: we observe Z_i=X_i+ε_i, where X_i is a stationary solution of the equation X_i=f_θ⁰(X_i-1)+ξ_i. The regression function f_θ⁰ is known up to a finite dimensional parameter θ⁰. The distributions of X₀ and ξ₁ are unknown whereas the distribution of ε₁ is completely known. We want to estimate the parameter θ⁰ by using the observations Z₀,..,Z_n. We propose an estimation procedure based on a modified least square criterion involving a weight function w, to be suitably chosen. We give upper bounds for the risk of the estimator, which depend on the smoothness of the errors density f_ε and on the smoothness properties of w f_θ.

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