Uniform-in-bandwidth nearest-neighbor density estimation

作者：Ouadah Sarah^*

来源：Statistics & Probability Letters, 2013, 83(8): 1835-1843.

DOI：10.1016/j.spl.2013.04.014

• Nonparametric density estimation
• Nearest-neighbor density estimator
• Uniform empirical quantile process
• Functional limit laws
• Convergence in probability

We present a sharp uniform-in-bandwidth limit law for the nearest-neighbor density estimator. Our result is established in the framework of convergence in probability, and we allow the bandwidth to vary within the complete range for which the estimator is consistent. We provide the explicit value of the asymptotic limiting constant for the uniform-in-bandwidth sup-norm of the estimator's random error.

• 出版日期2013-8