Exponential probability inequality for \(m\)-END random variables and its applications. (English) Zbl 1330.60031
Summary: The concept of \(m\)-extended negatively dependent (\(m\)-END, in short) random variables is introduced and the Kolmogorov exponential inequality for \(m\)-END random variables is established. As applications of the Kolmogorov exponential inequality, we further investigate the complete convergence for arrays of rowwise \(m\)-END random variables and the complete consistency for the estimator of nonparametric regression models based on \(m\)-END errors. Our results generalize and improve some known ones for independent random variables and dependent random variables.
MSC:
| 60E05 | Probability distributions: general theory |
| 60F15 | Strong limit theorems |
| 62G05 | Nonparametric estimation |
Keywords:
\(m\)-extended negatively dependent random variables; complete convergence; Kolmogorov exponential inequality; complete consistencyReferences:
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