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On semiparametric EV models with serially correlated errors in both regression models and measured covariates. (English) Zbl 1142.62043
The response \(y_i\) depends on the covariates \(\xi_k(t)\) and \(z_{ki}\) through the following linear regression model: \[ y_i=\beta_1\xi_1(t_i)+\dots+\beta_p\xi_p(t_i)+\alpha_1z_{1i}+\dots+a_qz_{qi} +\varepsilon_i. \] The variables \(y\), \(z\) and \(t\) are fully observed but \(\xi(t)\) is measured with errors: the observations are \(x_{ki}=\xi_k(t_i)+u_{ki}\). The errors \(\varepsilon_i\) are modelled by an autoregression model and \(u_{ki}\) are modelled by a vector autoregression. The authors describe a weighted estimating-equations based estimator for \(\alpha\) and \(\beta\) in which kernel smoothing is used to approximate \(\xi_k(t)\) and difference-based algorithms are applied for the estimation of the covariance structure of the errors. It is shown that the obtained estimates are asymptotically normal in \(\sqrt{n}\)-asymptotics. Results of simulations and an application to Microsoft stock data are presented.

MSC:
62J05 Linear regression; mixed models
62G08 Nonparametric regression and quantile regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G20 Asymptotic properties of nonparametric inference
62G05 Nonparametric estimation
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