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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.

##### MSC:
 62M09 Non-Markovian processes: estimation 62G05 Nonparametric estimation
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