Jonas Peters studies causal inference and the foundations of conditional independence testing. With Rajen D. Shah, he proved that a test with uniform finite-sample validity over an unrestricted continuous-data null class cannot obtain nontrivial power against alternatives in their setting.[ref]
The Hardness of Conditional Independence Testing and the Generalised Covariance Measure by Rajen D. Shah and Jonas Peters. Impossibility result and its distributional scope
Their constructive response is the generalized covariance measure statistic: regress each of two variables on the conditioning variables and examine the covariance of their residuals. Suitable regression-error rates and moment conditions yield asymptotic validity. Such a test targets conditional residual association; arbitrary forms of conditional dependence need not produce a nonzero residual covariance.[ref]
The Hardness of Conditional Independence Testing and the Generalised Covariance Measure by Rajen D. Shah and Jonas Peters. Section3.1 and asymptotic conditions
New to topics? Read the docs here!