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The James Webb Space Telescope will offer high-angular resolution observingcapability in the near-infrared with masking interferometry on NIRISS, andcoronagraphic imaging on NIRCam & MIRI. Full aperture kernel-phase basedinterferometry complements these observing modes, probing for companions atsmall separations while preserving the telescope throughput.  Our goal is to derive both theoretical and operational contrast detectionlimits for the kernel-phase analysis of JWST NIRISS full-pupil observations byusing tools from hypothesis testing theory, applied to observations of faintbrown dwarfs with this instrument, but the tools and methods introduced hereare applicable in a wide variety of contexts.  We construct a statistically independent set of observables fromaberration-robust kernel phases. Three detection tests based on theseobservable quantities are designed and analysed, all guaranteeing a constantfalse alarm rate for small phase aberrations. One of these tests, theLikelihood Ratio or Neyman-Pearson test, provides a theoretical performancebound for any detection test.  The operational detection method considered here is shown to exhibit onlymarginal power loss with respect to the theoretical bound. In principle, forthe test set to a false alarm probability of 1%, companion at contrastsreaching 10^3 at separations of 200 mas around objects of magnitude 14.1 aredetectable. With JWST NIRISS, contrasts of up to 10^4 at separations of 200 mascould be ultimately achieved, barring significant wavefront drift.  The proposed detection method is close to the ultimate bound and offersguarantees over the probability of making a false detection for binaries, aswell as over the error bars for the estimated parameters of the binariesdetectable by JWST NIRISS. This method is not only applicable to JWST NIRISSbut to any imaging system with adequate sampling.

Kernel-phase Detection Limits : Hypothesis Testing and the Example of JWST NIRISS Full Pupil Images