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Convergence of functional \(k\)-nearest neighbor regression estimate with functional responses. (English) Zbl 1274.62291

Summary: Let \((X_{1},Y_{1}),\ldots ,(X_{n},Y_{n})\) be independent and identically distributed random elements taking values in \(\mathcal F\times \mathcal H\), where \(\mathcal F\) is a semi-metric space and \(\mathcal H\) is a separable Hilbert space. We investigate the rates of strong (almost sure) convergence of the \(k\)-nearest neighbor estimate. We give two convergence results assuming a finite moment condition and exponential tail condition on the noises respectively, with the latter requiring less stringent conditions on \(k\) for convergence.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference

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References:

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