Efficient Interpolation of Density Estimators

• URL: http://arxiv.org/abs/2011.04922v1
• Date: Tue, 10 Nov 2020 06:05:00 GMT
• Title: Efficient Interpolation of Density Estimators
• Authors: Paxton Turner, Jingbo Liu, and Philippe Rigollet
• Abstract summary: We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. Our result gives a new statistical perspective on the problem of fast evaluation of kernel density estimators in the presence of underlying smoothness.
• Score: 23.154249845820306
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation scheme to give a computationally efficient construction that converts the original estimator to a new estimator that can be queried efficiently and has low space requirements, all without adversely deteriorating the original approximation quality. Our result gives a new statistical perspective on the problem of fast evaluation of kernel density estimators in the presence of underlying smoothness. As a corollary, we give a succinct derivation of a classical result of Kolmogorov---Tikhomirov on the metric entropy of H\"{o}lder classes of smooth functions.

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