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球面自回归模型及其在分布与成分时间序列中的应用AI 解读

We introduce a new class of autoregressive models for spherical time series. The dimension of the spheres on which the observations of the time series are situated may be finite-dimensional or infinite-dimensional, where in the latter case we consider the Hilbert sphere. Spherical time series arise in various settings. We focus here on distributional and compositional time series. Applying a square root transformation to the densities of the observations of a distributional…

自回归最优传输模型AI 解读

Abstract Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregressive models that operate in the space of optimal transport maps. The autoregressive transport models that we introduce here are based on regressing optimal transport maps…

Wasserstein 回归AI 解读

The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the Wasserstein metric, we develop a class of regression models for such data, where random distributions serve as predictors and the responses are either also distributions or scalars. To define this regression model, we use the geometry of…

Fréchet 变点检测AI 解读

We propose a method to infer the presence and location of change-points in the distribution of a sequence of independent data taking values in a general metric space, where change-points are viewed as locations at which the distribution of the data sequence changes abruptly in terms of either its Fréchet mean, Fréchet variance or both. The proposed method is based on comparisons of Fréchet variances before and after putative change-point locations and does not require a…

将风险率建模为函数型数据：队列生命表分析与死亡率预测AI 解读

As world populations age, the analysis of demographic mortality data and demographic predictions of future mortality have met with increasing interest. The study of mortality patterns and the forecasting of future mortality with its associated impacts on social welfare, health care, and societal planning has become a more pressing issue. An ideal set of data to study patterns of change in long-term mortality is the well-known historical Swedish cohort mortality data, because…