Kernel Density Estimation
The most classical nonparametric density estimation method, which places a kernel function, typically a symmetric probability density such as a Gaussian kernel, at each data point and sums and normalizes all kernel functions to obtain a density estimate. The convergence rate is determined by the bandwidth parameter, attaining the optimal rate of n^{-s/(2s+1)} for densities with smoothness s.
Timeline (last 90 days)
The paper proves that a continuous plug-in estimator based on kernel density estimation achieves the minimax rate n^{-s/(d+2s)} when the support manifolds are known.
Kernel density estimation achieves a convergence rate of n^{-s/(2s+1)} on densities with smoothness s.
In kernel density estimation (KDE), when the Gaussian kernel bandwidth parameter σ is too small the estimate degenerates into a collection of discrete points, while when σ is too large it over-smooths and loses detailed information, reflecting the bias-variance tradeoff.
All Facts (3)
The paper proves that a continuous plug-in estimator based on kernel density estimation achieves the minimax rate n^{-s/(d+2s)} when the support manifolds are known.
50%UnverifiedKernel density estimation achieves a convergence rate of n^{-s/(2s+1)} on densities with smoothness s.
50%UnverifiedIn kernel density estimation (KDE), when the Gaussian kernel bandwidth parameter σ is too small the estimate degenerates into a collection of discrete points, while when σ is too large it over-smooths and loses detailed information, reflecting the bias-variance tradeoff.
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