标题： 多小波密度估计 显示英文标题

标题： Multiwavelet density estimation

摘要： 精确的密度估计方法在许多科学领域中发挥着重要作用，其应用包括仿真模型、决策支持工具和探索性数据分析。 在过去，直方图和核密度估计器是最主要的选择工具，主要是因为它们易于使用且数学上简单。 最近，由于小波能够逼近一大类函数（包括具有局部剧烈变化的函数），利用小波进行密度估计的方法越来越受欢迎。 然而，众所周知，小波基的一个属性是它们无法同时具备对称性、正交性和紧支性。 多小波——一种更一般的向量值小波构造方式——克服了这一缺点，使其成为估计密度函数的自然选择，许多密度函数在诸如峰值等特征周围表现出局部对称性。 我们将小波密度估计方法扩展到使用多小波基，并展示了几个经验结果，表明在较粗分辨率水平上，多小波估计器的表现优于其对应的小波估计器。 显示英文摘要

摘要： Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel density estimators have been the predominant tools of choice, primarily due to their ease of use and mathematical simplicity. More recently, the use of wavelets for density estimation has gained in popularity due to their ability to approximate a large class of functions, including those with localized, abrupt variations. However, a well-known attribute of wavelet bases is that they can not be simultaneously symmetric, orthogonal, and compactly supported. Multiwavelets-a more general, vector-valued, construction of wavelets-overcome this disadvantage, making them natural choices for estimating density functions, many of which exhibit local symmetries around features such as a mode. We extend the methodology of wavelet density estimation to use multiwavelet bases and illustrate several empirical results where multiwavelet estimators outperform their wavelet counterparts at coarser resolution levels.