标题： 单纯形上强混合序列的 Dirichlet 核密度估计 显示英文标题

标题： Dirichlet kernel density estimation for strongly mixing sequences on the simplex

摘要： 本文首次研究了定义在单纯形上的成分数据的Dirichlet核密度估计量的理论性质，探讨了涉及时间相关观测且具有强混合条件的场景。 我们严格证明了这些估计量的渐近正态性和均方误差的结果，将之前独立同分布(iid)背景下的发现扩展到了更一般的强混合过程设定下。 为了展示其实际应用价值，该估计量被用于分析十二年间多个雷诺汽车车型月度市场份额组成的时序数据，带宽选择通过留一法最小二乘交叉验证完成。 我们的研究结果强调了当应用于具有时间依赖性的成分数据分析时，Dirichlet核方法的可靠性和有效性。 显示英文摘要

摘要： This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong mixing conditions. We establish rigorous results for the asymptotic normality and mean squared error of these estimators, extending previous findings from the independent and identically distributed (iid) context to the more general setting of strongly mixing processes. To demonstrate its practical utility, the estimator is applied to monthly market-share compositions of several Renault vehicle classes over a twelve-year period, with bandwidth selection performed via leave-one-out least squares cross-validation. Our findings underscore the reliability and strength of Dirichlet kernel techniques when applied to temporally dependent compositional data.