标题： 半参数马尔可夫模型用于多类型点模式 显示英文标题

标题： Semi-parametric Markov models for multi-type point patterns

摘要： 多类型马尔可夫点过程为建模复杂的多类型点模式提供了一个灵活的框架，其中需要捕捉点之间的相互作用以及依赖于观察协变量的大规模趋势。 然而，在存在未观察到的空间混杂因素的情况下，交互作用和协变量效应的估计可能会严重偏倚。 在本文中，我们引入了一类新的半参数马尔可夫点过程，该过程通过一个非参数因子来调整空间混杂因素，该因子能够容纳所有类型点共有的潜在空间变量的影响。 我们引入了一个条件伪似然函数用于参数估计，并证明了所得估计量具有理想的渐近性质。 我们的方法在产业集聚研究中尤其具有巨大潜力，我们将它应用于研究法国两种类型银行位置的空间模式。 显示英文摘要

摘要： Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates. However, estimation of interaction and covariate effects may be seriously biased in the presence of unobserved spatial confounders. In this paper we introduce a new class of semi-parametric Markov point processes that adjusts for spatial confounding through a non-parametric factor that accommodates effects of latent spatial variables common to all types of points. We introduce a conditional pseudo likelihood for parameter estimation and show that the resulting estimator has desirable asymptotic properties. Our methodology not least has great potential in studies of industry agglomeration and we apply it to study spatial patterns of locations of two types of banks in France.