A semiparametric latent factor model for large scale temporal data with heteroscedasticity
A semiparametric latent factor model for large scale temporal data with heteroscedasticity
复制标题
DOI：
10.1016/j.jmva.2021.104786
复制
发表时间：
2021-11
期刊：
影响因子：
--
通讯作者：
Lyuou Zhang;Wen Zhou;Haonan Wang
中科院分区：
文献类型：
--
作者：
Lyuou Zhang;Wen Zhou;Haonan Wang
大规模时态数据在众多的应用中得到了蓬勃发展，其复杂的结构，特别是具有时间内和时间间相关性的主题之间的异方差性，激发了对新的统计模型的巨大需求。在本文中，我们考虑了一个灵活的模型，大规模的时间数据与特定主题的异方差的协变量信息。形式上，该模型采用潜在的半参数因素，同时考虑到特定主题的异方差和同期和/或串行相关性。被试特异性异方差被建模为未观测因子过程和协变量效应的乘积，并通过加性模型进一步表征。对于估计，我们提出了一个两步的程序。首先，潜在的因素过程和非参数加载恢复，通过基于投影的方法，然后，我们估计的回归分量的方法从广义最小二乘激励。通过仔细检查恢复因子过程及其负荷的非渐近速率，我们显示了在没有潜在因子过程和受试者的协变量效应的先验知识的情况下估计的回归系数的一致性和效率。即使对于有限的时间点，统计保证仍然有效，这使得我们的方法在受试者数量显著超过观察时间点时特别有吸引力。使用全面的模拟，我们证明了我们的方法，这证实了理论研究结果的有限样本性能。最后，我们将我们的方法应用于2015年在美国129个监测点收集的空气质量和能源消耗数据集。
Large scale temporal data have flourished in a vast array of applications, and their sophisticated structures, especially the heteroscedasticity among subjects with inter- and intra-temporal dependence, have fueled a great demand for new statistical models. In this paper, with covariate information, we consider a flexible model for large scale temporal data with subject-specific heteroscedasticity. Formally, the model employs latent semiparametric factors to simultaneously account for the subject-specific heteroscedasticity and the contemporaneous and/or serial correlations. The subject-specific heteroscedasticity is modeled as the product of the unobserved factor process and subject’s covariate effect, which is further characterized via additive models. For estimation, we propose a two-step procedure. First, the latent factor process and nonparametric loading are recovered through projection-based methods, and following, we estimate the regression components by approaches motivated from the generalized least squares. By scrupulously examining the non-asymptotic rates for recovering the factor process and its loading, we show the consistency and efficiency of estimated regression coefficients in the absence of prior knowledge of latent factor process and subject’s covariate effect. The statistical guarantees remain valid even for finite time points that makes our method particularly appealing when the subjects significantly outnumber the observation time points. Using comprehensive simulations, we demonstrate the finite sample performance of our method, which corroborates the theoretical findings. Finally, we apply our method to a data set of air quality and energy consumption collected at 129 monitoring sites in the United States in 2015.