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Title: A general central limit theorem and subsampling variance estimator for alpha-mixing multivariate point processes Authors:  Christophe Biscio - Aalborg University (Denmark) [presenting]
Abstract: Central limit theorems for multivariate summary statistics of alpha-mixing spatial point processes have usually been established using either the so-called Bernstein's blocking technique or an approach based on Bolthausen's results. It is characteristic that essentially the same theorems have been (re)-invented again and again for different specific settings and statistic considered. Moreover, although there exists estimates in some particular cases, the asymptotic variance is usually unknown or difficult to compute. We present a unified framework based on Bolthausen's work to state, once and for all, a general central limit theorem for alpha-mixing multivariate point process that applies in a general non-stationary setting and is also applicable to non-parametric kernel estimators depending on a bandwidth converging to zero. In particular, we argue why this approach is more suitable than the one using Bernstein's blocking technique. We believe this can save a lot of work and tedious repetitions in future applications of alpha-mixing point processes.