Time-of-flight measurements of high-energy astrophysical neutrinos can be used to probe Lorentz invariance, a pillar of modern physics. If Lorentz-invariance violation (LIV) occurs, it could cause neutrinos to slow down, with the delay scaling linearly or quadratically with their energy. We introduce nonparametric statistical methods designed to detect LIV-induced distortions in the temporal structure of a high-energy neutrino flare as it travels to Earth from a distant astrophysical source, independently of the intrinsic timing properties of the source. Our approach, illustrated using the $2014/2015\mathrm{TeV}\text{−}\mathrm{PeV}$ neutrino flare from the blazar TXS $0506+056$ detected by IceCube, finds that the LIV energy scale must exceed ${10}^{14}\mathrm{GeV}$ (linear) or ${10}^9\mathrm{GeV}$ (quadratic). Our methods provide a robust means to investigate LIV by focusing solely on a neutrino flare without relying on electromagnetic counterparts and to account for realistic energy and directional uncertainties. For completeness, we compare our limits inferred from TXS $0506+056$ to the sensitivity inferred from multimessenger detection of tentative coincidences between neutrinos and electromagnetic emission from active galactic nuclei and tidal disruption events.

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• Cosmic ray & astroparticle detectors
• Extrasolar neutrino astronomy
• Particle astrophysics
• Quantum gravity
• Transient & explosive astronomical phenomena