ABSTRACT Kernel density estimation has been applied in many computational subjects. In this paper, we propose a density estimation procedure from a Bayesian nonparametric perspective using Dirichlet process prior for the length-biased data under an unknown kernel function. In this situation, the kernel within the Dirichlet process mixture model will be approximated by the kernel density estimator. We present a Bayesian nonparametric method for finding the bandwidth parameter in the kernel density estimation using a Markov chain Monte Carlo approach. Then, this approach is used to the simulated and real data set. Finally, we compare the proposed bandwidth estimation with the other estimations like cross-validation and Bayes based on the mean integrated squared error criterion.

中文翻译：

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使用混合核估计器对长度偏置数据进行贝叶斯非参数带宽估计

摘要 核密度估计已应用于许多计算学科。在本文中，我们从贝叶斯非参数角度提出了一种密度估计程序，使用 Dirichlet 过程先验对未知核函数下的长度偏置数据。在这种情况下，狄利克雷过程混合模型中的核将被核密度估计器近似。我们提出了一种贝叶斯非参数方法，用于使用马尔可夫链蒙特卡罗方法在核密度估计中找到带宽参数。然后，将该方法用于模拟和真实数据集。最后，我们将所提出的带宽估计与基于均值积分平方误差准则的其他估计（如交叉验证和贝叶斯）进行比较。