On the rate of convergence of empirical distribution functions in \(AR(1)\) models (Q2739833)
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scientific article; zbMATH DE number 1646310
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rate of convergence of empirical distribution functions in \(AR(1)\) models |
scientific article; zbMATH DE number 1646310 |
Statements
16 September 2001
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residual distribution
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autoregression
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nonparametric estimation
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uniform confidence intervals
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0.9078616
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0.8957879
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0.89081395
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On the rate of convergence of empirical distribution functions in \(AR(1)\) models (English)
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The author considers an \(AR(1)\) process \(U_k=\beta U_{k-1}+\varepsilon_k\), where \(\varepsilon_k\) are i.i.d. with d.f. \(G\). The unknown \(G\) is estimated by the empirical distribution function of the residuals \(G_n\). The author derives an upper bound for NEWLINE\[NEWLINE\Pr\{\sup_x\sqrt{n}|G_n(x)-G(x)|>\varepsilon\},NEWLINE\]NEWLINE for the case when NEWLINE\[NEWLINE\sup_x|G''(x)|<\infty,\quad E\varepsilon_n^4<\infty,\quad |\beta|\leq\Lambda<1.NEWLINE\]
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