Asymptotic properties of Dirichlet kernel density estimators
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DOI: 10.1016/j.jmva.2021.104832
Abstract: We study theoretically, for the first time, the Dirichlet kernel estimator introduced by Aitchison and Lauder [3] for the estimation of multivariate densities supported on the d-dimensional simplex. The simplex is an important case as… read more here.
Keywords: kernel density; dirichlet kernel; density estimators; kernel estimator ... See more keywords
Strong Lp convergence of wavelet deconvolution density estimators
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DOI: 10.1142/s0219530517500154
Abstract: Using compactly supported wavelets, Gine and Nickl [Uniform limit theorems for wavelet density estimators, Ann. Probab. 37(4) (2009) 1605ā1646] obtain the optimal strong Lā(ā) convergence rates of wavelet estimators for a fixed noise-free density function.… read more here.
Keywords: density estimators; density; convergence wavelet; convergence ... See more keywords
On the Study of Multiwavelet Deconvolution Density Estimators
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DOI: 10.1155/2020/4259373
Abstract: In this paper, multiwavelet deconvolution density estimators are presented by a linear multiwavelet expansion and a nonlinear multiwavelet expansion, respectively. Moreover, the unbiased estimation is shown, and asymptotic normality is discussed for the multiwavelet deconvolution… read more here.
Keywords: deconvolution density; multiwavelet deconvolution; density estimators;
Optimal exponential bounds for aggregation of density estimators
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DOI: 10.3150/15-bej742
Abstract: We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential… read more here.
Keywords: aggregation density; density estimators; density; optimal exponential ... See more keywords