A new technique for calibrating Tully-Fisher like relations was proposed. Based on a null-correlation approach, this calibration procedure is efficient when galaxies constituting the calibration sample are homogeneously distributed in space. The NCA technique is thus adequate for calibrating a sample of field galaxies for example.

In a first step was introduced
the random variable
dependent on a slope parameter *a* and on the
observed apparent
magnitude *m*, log line-width distance indicator *p*
and redshift *z*.
In the case of pure Hubble flow (i.e. radial peculiar velocities
are null everywhere), it was shown that variables *p* and
*X*(*a*) are not correlated if and only if parameter *a*
equals the slope *a*^{D} of the Direct TF relation.
The NCA estimate of the DTF slope *a*^{D} was defined
as the value of *a* such that correlation between *p*
and *X*(*a*) vanishes.
This estimator of *a*^{D} was found particularly robust since it
does not depend on the selection effects on
*m* and *p* which affect the observed calibration sample
and on the specific shape of the luminosity
function.

Influences of radial peculiar velocities was investigated
in a second step. It was shown that the presence
of a peculiar velocity field biases the NCA estimate of *a*^{D}.
A procedure which
consists in discarding nearby galaxies
of the observed sample was introduced.
Such subsampling is achieved by adding an
extra selection function in distance estimate . The
magnitude of the bias and its variations in function of
the cut-off in distance estimate *r*^{*} have been analysed
on a synthetic sample and on the Mathewson spirals field galaxies
sample (see Appendix D). The proposed
subsampling procedure
looks fairly efficient for minimizing bias on the
NCA estimate of the DTF slope *a*^{D} created by the presence
of radial peculiar velocities.

In the third step, calibration of the "zero-point"
parameter *B*^{*} entering the definition of the velocity
estimator was
investigated. It was shown that
the variables *p* and
are not correlated if and only if parameter
equals the "zero-point" *B*^{*}.
The NCA estimate of the second calibration parameter
*B*^{*} was thus defined
as the value of such that correlation between *p*
and vanishes.
This *B*^{*} estimator is robust. It is
insensitive to observational selection effects
on *m* and *p* and to the specific shape of the
luminosity function.
Moreover, NCA estimate of *B*^{*} is not biased by the presence
of a Maxwellian velocity agitation nor by the
existence of bulk flow.

*Acknowledgements*

This work is one of the achievements of a long range program focusing on the statistical modelization of TF like relations, launched five years ago by Roland Triay. He is kindly thanked for constructive discussions. The hospitality of the Centre de Physique Théorique of Luminy is recognized. Stéphane Rauzy is cheerfully thanked for a generous financial support.

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