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Effective interpolations for kernel density estimators. (English) Zbl 0914.62027

Summary: We introduce a general interpolation scheme to be applied in the kernel density estimation. Our scheme is based on a piecewise higher-degree polynomial interpolation with a strategically chosen set of interpolation points. It is found that our interpolation scheme improves on the kernel density estimation in terms of the integrated mean squared error. A multivariate extension of our findings shows that the improvement increases substantially with the data dimension. In addition to the theoretical improvement, it is demonstrated that our interpolation scheme brings about a considerable computational saving over the original kernel density estimator, making itself comparable to the binning technique in the computational efficiency.

MSC:

62G07 Density estimation
65D05 Numerical interpolation
65C99 Probabilistic methods, stochastic differential equations
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References:

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