This article presents two generalized nonparametric methods for estimating multiple, possibly like, densities. The first generalization contains the Nadaraya–Watson estimator, the Jones et al. (Biometrika 82(2):327–338, 1995) bias reduction estimator, and Ker (Stat Probab Lett 117:23–30, 2016) possibly similar estimator as special cases. The second generalization contains the Nadaraya–Watson estimator, Ker (2016) possibly similar estimator, and the conditional density estimator of Hall et al. (J Am Stat Assoc 99(468):1015–1026, 2004) as special cases. The generalizations do not require knowledge of the form or extent of likeness between the unknown densities; an attractive feature in empirical applications. Numerical simulations demonstrate that the two proposed generalizations lead to significant efficiency gains.

本文介绍了两种用于估计多个（可能类似）密度的广义非参数方法。第一个概括包括Nadaraya–Watson估计量，Jones等。（Biometrika 82（2）：327-338，1995）偏差减少估计量，而Ker（Stat Probab Lett 117：23-30，2016）可能与特例相似。第二种概括包括Nadaraya–Watson估计量，Ker（2016）可能类似的估计量，以及Hall等人的条件密度估计量。（J Am Stat Assoc 99（468）：1015-1026，2004）为特例。概括不需要知道未知密度之间的相似形式或程度。在经验应用中具有吸引力。数值模拟表明，所提出的两个概括可显着提高效率。