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Strong consistency and rates for recursive probability density estimators of stationary processes. (English) Zbl 0619.62079
Authors’s abstract: Let \(\{X_ j\}^{\infty}_{j=-\infty}\) be a vector-valued stationary process with a first-order univariate probability density f on \({\mathbb{R}}^ d\). Recursive estimation of f(x) from n not necessarily independent observations \(\{X_ j\}^ n_{j=1}\) is considered. For processes \(\{X_ j\}^{\infty}_{j=-\infty}\) which are asymptotically uncorrelated, sharp rates for the almost sure convergence of kernel-type estimators \(f_ n(x)\) are established.

62M09 Non-Markovian processes: estimation
62G05 Nonparametric estimation
Full Text: DOI
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