We investigate regression adjustment via a recovered latent variable, termed substitute adjustment, and we give theoretical results to support that substitute adjustment estimates adjusted regression parameters when the observed regressors are conditionally independent given the latent variable. We derive finite sample bounds and asymptotic results supporting substitute adjustment estimation in the case where the latent variable takes values in a finite set.
The recently introduced graphical continuous Lyapunov models provide a new approach to statistical modeling of correlated multivariate data. The models view each observation as a one-time cross-sectional snapshot of a multivariate dynamic process in …
We develop a model-free framework based on the Local Covariance Measure for testing the hypothesis that a counting process is conditionally locally independent of another process. We propose the (cross-fitted) Local Covariance Test, and we show that its level and power can be controlled uniformly, provided that two nonparametric estimators are consistent with modest rates.
We develop a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric residuals.