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Kernel Choice Matters for Local Polynomial Density Estimators at Boundaries

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  • Shunsuke Imai
  • Yuta Okamoto

Abstract

Local polynomial density (LPD) estimators are widely used for inference on boundary features of the density function. Contrary to conventional wisdom, we show that kernel choice substantially affects efficiency. Theory, simulations, and empirical evidence indicate that the popular triangular kernel delivers large mean squared error, wide confidence intervals, and limited power for detecting discontinuities. Moreover, small-sample variance can explode because the finite-sample variance is infinite under compactly supported kernels. As a simple yet powerful remedy, we recommend using the Gaussian or Laplace kernels. These alternatives yield marked efficiency gains and eliminate variance explosions, improving the reliability of LPD-based inference.

Suggested Citation

  • Shunsuke Imai & Yuta Okamoto, 2023. "Kernel Choice Matters for Local Polynomial Density Estimators at Boundaries," Papers 2306.07619, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2306.07619
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