  Spontaneous breaking of Lorentz symmetry at energies on the order of the
Planck energy or lower is predicted by many quantum gravity theories, implying
non-trivial dispersion relations for the photon in vacuum. Consequently,
gamma-rays of different energies, emitted simultaneously from astrophysical
sources, could accumulate measurable differences in their time of flight until
they reach the Earth. Such tests have been carried out in the past using fast
variations of gamma-ray flux from pulsars, and more recently from active
galactic nuclei and gamma-ray bursts. We present new constraints studying the
gamma-ray emission of the galactic Crab Pulsar, recently observed up to TeV
energies by the MAGIC collaboration. A profile likelihood analysis of pulsar
events reconstructed for energies above 400GeV finds no significant variation
in arrival time as their energy increases. Ninety-five percent~CL limits are
obtained on the effective Lorentz invariance violating energy scale at the
level of $E_{\mathrm{QG}_1} > 5.5\cdot 10^{17}$GeV ($4.5\cdot 10^{17}$GeV) for
a linear, and $E_{\mathrm{QG}_2} > 5.9\cdot 10^{10}$GeV ($5.3\cdot 10^{10}$GeV)
for a quadratic scenario, for the subluminal and the superluminal cases,
respectively. A substantial part of this study is dedicated to calibration of
the test statistic, with respect to bias and coverage properties. Moreover, the
limits take into account systematic uncertainties, found to worsen the
statistical limits by about 36--42\%. Our constraints would have resulted much
more competitive if the intrinsic pulse shape of the pulsar between 200GeV and
400GeV was understood in sufficient detail and allowed inclusion of events well
below 400GeV.
