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2017 Nonparametric estimating equations for circular probability density functions and their derivatives
Marco Di Marzio, Stefania Fensore, Agnese Panzera, Charles C. Taylor
Electron. J. Statist. 11(2): 4323-4346 (2017). DOI: 10.1214/17-EJS1318


We propose estimating equations whose unknown parameters are the values taken by a circular density and its derivatives at a point. Specifically, we solve equations which relate local versions of population trigonometric moments with their sample counterparts. Major advantages of our approach are: higher order bias without asymptotic variance inflation, closed form for the estimators, and absence of numerical tasks. We also investigate situations where the observed data are dependent. Theoretical results along with simulation experiments are provided.


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Marco Di Marzio. Stefania Fensore. Agnese Panzera. Charles C. Taylor. "Nonparametric estimating equations for circular probability density functions and their derivatives." Electron. J. Statist. 11 (2) 4323 - 4346, 2017.


Received: 1 July 2016; Published: 2017
First available in Project Euclid: 13 November 2017

zbMATH: 1383.62096
MathSciNet: MR3724222
Digital Object Identifier: 10.1214/17-EJS1318

Keywords: Circular kernels , Density estimation , Fourier coefficients , jackknife , sin-polynomials , trigonometric moments , von Mises density


Vol.11 • No. 2 • 2017
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