AI 中文总结
针对因多种限制而只能获取分组数据的情况，研究提出均值调整对数凹（MALC）密度估计方法，该方法无带宽且不依赖特定分布假设，通过模拟评估其性能，结果显示此方法在分组数据分析中稳健有效，应用范围更广。
AI 中文摘要
在某些情况下，由于实验报告的不确定性、间歇性测量、保密性和未检测到的数据等系统和技术限制，数据可能无法以传统格式获取，而是以分组形式呈现，即仅知道区间内的出现次数。挑战在于基于观察到的分组数据估计底层未分组数据的密度，且无关于底层分布的信息。本研究引入一种用于单变量分组数据的均值调整对数凹（MALC）密度估计方法，旨在提供一种不依赖特定分布假设的无带宽非参数方法。通过对不同分布、不同样本大小和网格宽度进行模拟来评估MALC方法的性能。结果证明了MALC方法在分组数据分析中的稳健性和有效性，比传统方法有更广泛的应用。
英文摘要
In some situations, data is collected under systematical and technical constraints due to uncertainty in experimental reports, intermittent measurements, confidentiality, and non-detects. For this reason, it might not be possible to retrieve or receive the data in a conventional format but rather in a grouped form where only the number of occurrences is known within intervals. The challenge is to estimate the density of the underlying ungrouped data based on the observed grouped data with no information regarding the underlying distribution. To overcome this problem, this study introduces a mean-adjusted log-concave (MALC) density estimation method for univariate grouped data, aiming to provide a bandwidth-free non-parametric approach that does not rely on specific distributional assumptions. The performance of the MALC method is evaluated through simulations across various distributions with different sample sizes and grid widths. The results demonstrate the robustness and effectiveness of the MALC approach in grouped data analysis, offering a broader range of applications over traditional methods.
