On shrinking minimax convergence in nonparametric statistics

Sam Efromovich

Journal of Nonparametric Statistics, 2014, vol. 26, issue 3, 555-573

Abstract: ... if we are prepared to assume that the unknown density has k derivatives, then ... the optimal mean integrated squared error is of order n -super- - 2 k /(2 k +1) ... ' The citation is from Silverman [(1986), Density Estimation for Statistics and Data Analysis , London: Chapman & Hall] and its assertion is based on a classical minimax lower bound which is the pillar of the modern nonparametric statistics. This paper proposes a new minimax methodology that implies a faster decreasing minimax lower bound that is attainable by a data-driven estimator, and the same estimator is also minimax under the classical approach. The recommendation is to test performance of estimators via the new and classical minimax approaches.

Date: 2014
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DOI: 10.1080/10485252.2014.931394

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