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A general result on complete convergence for weighted sums of linear processes and its statistical applications. (English) Zbl 1418.62073

Summary: Consider the linear process \(X_1=\sum^\infty_{j=-\infty}\psi_j e_{i-j}\), where \(\{e_i\}\) is a sequence of identically distributed, negatively associated random variables with \(Ee_0=0\), and \(\{\psi_j\}\) is a sequence of real numbers with \(\sum^\infty_{j=-\infty} |\psi_j|<\infty\). Under some mild conditions, we first establish a general result on complete convergence for weighted sums of such linear process, and then describe its statistical properties and interpretations in both semiparametric and nonparametric regression models. We also prove the complete consistency for the parameter estimators. In addition, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.

MSC:

62G08 Nonparametric regression and quantile regression
62F12 Asymptotic properties of parametric estimators
62G20 Asymptotic properties of nonparametric inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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