  More than two hundred classical cepheids were measured by the Hipparcos
astrometric satellite, making possible a geometrical calibration of the cepheid
distance scale. However, the large average distance of even the nearest
cepheids measured by Hipparcos implies trigonometric parallaxes of at most a
few mas. Determining unbiased distances and absolute magnitudes from such high
relative error parallax data is not a trivial problem.In 1997, Feast &
Catchpole announced that Hipparcos cepheid parallaxes indicated a
Period-Luminosity scale 0.2 mag brighter than previous calibrations, with
important consequences on the whole cosmic distance scale. In the wake of this
initial study, several authors have reconsidered the question, and favour
fainter calibrations of cepheid luminositites, compatible with pre-Hipparcos
values. All authors used equivalent data sets, and the bulk of the difference
in the results arises from the statistical treatment of the parallax data. We
have attempted to repeat the analyses of all these studies and test them with
Monte Carlo simulations and synthetic samples. We conclude that the initial
Feast & Catchpole study is sound, and that the subsequent studies are subjected
in several different ways to biases involved in the treatment of high relative
error parallax data. We consider the source of these biases in some detail. We
also propose a reappraisal of the error budget in the final Hipparcos cepheid
result, leading to a PL relation -- adapted from Feast & Catchpole -- of
M_V=-2.81 (assumed) log P -1.43 +-0.16 (stat) +0-0.03 (syst). We compare this
calibration to recent values from cluster cepheids or the surface brightness
method, and find that the overall agreement is good within the uncertainties.
