Abstract
We review the scheme introduced by Kim and Richards for deconvolution density estimation on compact Lie groups. The Fourier transform is used to express the problem in terms of products of matrices of irreducible representations. We introduce a sequence of consistent estimators, by taking cut-offs in a certain Fourier expansion. Some smoothness classes of noise are discussed and used to find optimal rates of convergence of the estimators.
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Notes
- 1.
For background on kernel density estimation, see e.g. Silverman [186].
- 2.
Recall that if \(Z:\Omega \rightarrow \mathbb {C}\) is a complex-valued random variable, then its variance, Var\((Z):=\mathbb {E}(|Z|^{2}) - |\mathbb {E}(Z)|^{2}\).
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© 2014 Springer International Publishing Switzerland
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Applebaum, D. (2014). Deconvolution Density Estimation. In: Probability on Compact Lie Groups. Probability Theory and Stochastic Modelling, vol 70. Springer, Cham. https://doi.org/10.1007/978-3-319-07842-7_6
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DOI: https://doi.org/10.1007/978-3-319-07842-7_6
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07841-0
Online ISBN: 978-3-319-07842-7
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