TY - JOUR

T1 - Nonparametric conditional local independence testing

AU - Christgau, Alexander Mangulad

AU - Petersen, Lasse

AU - Hansen, Niels Richard

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2023.

PY - 2023

Y1 - 2023

N2 - Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional processes, and it is important for the description and learning of causal relations among processes.We develop a model-free framework for testing the hypothesis that a counting process is conditionally locally independent of another process. To this end, we introduce a new functional parameter called the Local Covariance Measure (LCM), which quantifies deviations from the hypothesis. Following the principles of double machine learning, we propose an estimator of the LCM and a test of the hypothesis using nonparametric estimators and sample splitting or cross-fitting. We call this test the (cross-fitted) Local Covariance Test ((X)-LCT), and we show that its level and power can be controlled uniformly, provided that the nonparametric estimators are consistent with modest rates.We illustrate the theory by an example based on a marginalized Cox model with time-dependent covariates, and we show in simulations that when double machine learning is used in combination with cross-fitting, then the test works well without restrictive parametric assumptions.

AB - Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional processes, and it is important for the description and learning of causal relations among processes.We develop a model-free framework for testing the hypothesis that a counting process is conditionally locally independent of another process. To this end, we introduce a new functional parameter called the Local Covariance Measure (LCM), which quantifies deviations from the hypothesis. Following the principles of double machine learning, we propose an estimator of the LCM and a test of the hypothesis using nonparametric estimators and sample splitting or cross-fitting. We call this test the (cross-fitted) Local Covariance Test ((X)-LCT), and we show that its level and power can be controlled uniformly, provided that the nonparametric estimators are consistent with modest rates.We illustrate the theory by an example based on a marginalized Cox model with time-dependent covariates, and we show in simulations that when double machine learning is used in combination with cross-fitting, then the test works well without restrictive parametric assumptions.

KW - double machine learning

KW - functional CLT

KW - local independence

KW - Nonparametric inference

KW - stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85181889589&partnerID=8YFLogxK

U2 - 10.1214/23-AOS2323

DO - 10.1214/23-AOS2323

M3 - Journal article

AN - SCOPUS:85181889589

VL - 51

SP - 2116

EP - 2144

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 5

ER -