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The asymptotic variance of the continuous-time kernel estimator with applications to bandwidth selection. (English) Zbl 0984.62029

Summary: We derive simple expressions for the asymptotic variance of the kernel-density estimator of a stationary continuous-time process in one and \(d\) dimensions and relate convergence rates to sample path smoothness. Important applications include methods for selecting optimal smoothing parameters and construction of confidence bands for testing hypotheses about the density. In a simulation study the results are applied to bandwidth selection for discrete-time processes that can be modelled as continuous-time processes sampled at a high rate.

MSC:

62G07 Density estimation
62M09 Non-Markovian processes: estimation
62G20 Asymptotic properties of nonparametric inference

Software:

KernSmooth
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