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Estimation in mode regression is usually implemented via kernel density estimation or empirical likelihood methods, and its statistical properties are more complex than those of mean regression, with the convergence rate depending on the curvature of the density near the peak.
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10/27/2026
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UnverifiedIf the covariate density has spikes, discontinuities or holes near the target point, the local effective sample size is far below the global sample size, and the effective rate of pointwise estimation may be dominated by the smoothness of that local design rather than by the total sample size.72% similarUnverifiedIn 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.71% similarUnverifiedThe curse of dimensionality refers to the fact that as the covariate dimension d increases, the sample size required for non-parametric estimation grows exponentially, causing methods such as kernel density estimation and kernel mean embedding to lose practical convergence rates.71% similarUnverifiedPrevious generalization analyses of flow matching/diffusion models often required strong restrictive assumptions on the estimated velocity field, such as global Lipschitz continuity, bounded norm, or specific regularity conditions.69% similarUnverifiedA larger smoothness parameter β indicates a smoother density function, theoretically enabling better estimation accuracy with fewer samples.69% similar
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