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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]

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]

Rajen D. Shah develops statistical inference for high-dimensional data. His author publication list verifies work on regression, model checking and testing conditional independence.^[ref]

With Jonas Peters, he introduced the generalized covariance measure statistic, based on the covariance of residuals after each response is regressed on the same conditioning variables. The resulting hypothesis test combines regression estimates with a calibrated covariance statistic. Their accompanying impossibility result explains why unrestricted distribution-free conditional independence testing needs additional structure; the regression-based method instead states approximation and moment assumptions explicitly.^[ref]

By Rajen D. Shah and Jonas Peters. Annals of Statistics 48(3) (2020), 1514–1538. DOI: doi.org/10.1214/19-AOS1857

Author preprint: arxiv.org/abs/1804.07203 (the inspected PDF is version 6, dated March 2022). Locator: §3.1, definition of the univariate statistic and conditions for its asymptotic normality.