Title: Theory and inference for multivariate autoregressive binary models with an application to absence-presence data in ecology Show Chinese title

Title: 多变量自回归二元模型的理论与推断及其在生态学中缺失-存在数据的应用

Abstract: We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for such models is almost automatic and does not require parameter restrictions when the noise term is not compactly supported. We then study in details statistical inference in a dynamic version of a multivariate probit type model, as a particular case of our general construction. To avoid a complex likelihood optimization, we combine pseudo-likelihood and pairwise likelihood methods for which asymptotic results are obtained for a single path analysis and also for panel data, using ergodic theorems for multi-indexed partial sums. The latter scenario is particularly important for analyzing absence-presence of species in Ecology, a field where data are often collected from surveys at various locations. Our results also give a theoretical background for such models which are often used by the practitioners but without a probabilistic framework. Show Chinese abstract

Abstract: 我们引入了一类广义的自回归模型，用于研究具有平稳外生协变量的多元二元时间序列的动态特性。 在一组高层假设下，我们证明了此类模型存在平稳路径几乎是自动的，并且当噪声项不紧支撑时不需要参数限制。 然后，我们详细研究了动态多元概率模型中的统计推断，作为我们一般构造的一个特例。 为了避免复杂的似然优化，我们结合了伪似然和成对似然方法，对于单个路径分析和面板数据，利用多索引部分和的遍历定理得到了渐近结果。 后一种情况在生态学中分析物种的有无特别重要，这是一个数据通常从不同地点的调查中收集的领域。 我们的结果还为这些模型提供了理论基础，这些模型经常被实践者使用，但缺乏概率框架。