Finite-sample calibration and extensions of PSI-SINDy

Establish finite-sample calibration for PSI-SINDy and extend its inferential guarantees from scalar trajectories, fixed polynomial libraries, and independent Gaussian noise with known variance to multistate systems, broader candidate libraries, dependent noise, and estimated noise variance.

Background

PSI-SINDy provides finite-sample exact conditional inference for an auxiliary realized instrumental-variable coefficient and asymptotically valid inference for the selected-model best linear approximation coefficient under a restricted theoretical setting. The stated setting assumes scalar trajectories, fixed polynomial libraries, independent Gaussian measurement noise, and known noise variance.

The paper explicitly identifies unresolved limitations in both calibration and scope. In particular, finite-sample calibration for the primary selected-model BLA inference is not established generally, and the theoretical framework has not yet been extended to multistate systems, broader libraries, dependent noise, or the practically relevant case of an estimated noise variance.