Primary Submission Category: Dynamic Treatment Regimes
Causality with aging: Estimation and inference in a dynamic directed acyclic VAR graph with aging and subaging
Authors: Andrej Srakar,
Presenting Author: Andrej Srakar*
Directed acyclic graphs have seldom been studied in a dynamic context. We include stochastic aging in vector autoregression form for causal time-series. Let
(G = (mathcal{V,E)}) be a graph, and let (E = {{ E_{i}}}_{i in mathcal{V}}) be collection of i.i.d. random variables indexed by vertices of graph with exponential distribution with mean (1). We consider continuous-time Markov chain (X(t)) with state space (mathcal{V}). Transition rates are (w_{ij} = nuexpleft( – betaleft( (1 – a)E_{i} – aE_{j} right) right)). Proving an aging result consists in finding two-point function
(F(t_{w},t_{w} + t)) such that nontrivial limit(lim_{t rightarrow infty,frac{t}{t_{w}} = theta}{F(t_{w},t_{w} + t)} = F(theta)) exists. We consider VAR-based dynamic DAG combined with trap aging model above and prove results on aging and subaging. We propose causal estimators in this context and study their inferential properties. In application we study causal effects of early life education on health of an older person. Our novel approach is the first to include aging phenomena in causal inference and has applications among other in economics and health. We consider extensions to more complex causal time-series structures and to elephant random walk possibilities.