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Optimal Rates of Convergence for Nonparametric Deconvolution Problems
The optimal rates of convergence for nonparametric deconvolution problems depend on the smoothness of error distributions. According to the research, there are two types of optimal rates of convergence:
* Ordinary Smooth Error Distributions: For these cases, the optimal rate of convergence is achieved by deconvolution kernel density estimators.
* Supersmooth Error Distributions: In this case, the optimal rate of convergence can also be achieved by deconvolution kernel density estimators.
The difficulty of deconvolution problems increases with the smoothness of error distributions. The research paper states that "the smoother, the harder" (Source: On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems).
Reference:
* Fan, Jianqing (1991). "On the optimal rates of convergence for nonparametric deconvolution problems". The Annals of Statistics. 19 (3): 1257–1272.
Last Updated: February 22, 2026
The optimal rates of convergence for nonparametric deconvolution problems depend on the smoothness of error distributions. According to the research, there are two types of optimal rates of convergence:
* Ordinary Smooth Error Distributions: For these cases, the optimal rate of convergence is achieved by deconvolution kernel density estimators.
* Supersmooth Error Distributions: In this case, the optimal rate of convergence can also be achieved by deconvolution kernel density estimators.
The difficulty of deconvolution problems increases with the smoothness of error distributions. The research paper states that "the smoother, the harder" (Source: On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems).
Reference:
* Fan, Jianqing (1991). "On the optimal rates of convergence for nonparametric deconvolution problems". The Annals of Statistics. 19 (3): 1257–1272.
Last Updated: February 22, 2026
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