Asymptotic properties of the recursive kernel density estimate for extended negatively dependent samples
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Let $\{X_n, n\geq1\}$ be an extended negatively dependent random sequence with a common unknown density $f(x)$. In this paper, a kind of recursive kernel estimator of $f(x)$ is considered. The rate of uniformly strong consistency for the recursive kernel estimator is established under certain conditions, and the asymptotic normality of the recursive kernel estimator is also investigated. Some simulations are also presented to assess the validity of these theoretical results.
Abstract
Let $\{X_n, n\geq1\}$ be an extended negatively dependent random sequence with a common unknown density $f(x)$. In this paper, a kind of recursive kernel estimator of $f(x)$ is considered. The rate of uniformly strong consistency for the recursive kernel estimator is established under certain conditions, and the asymptotic normality of the recursive kernel estimator is also investigated. Some simulations are also presented to assess the validity of these theoretical results.