Determination of HII region metallicity in the context of estimating the
  primordial helium abundance
  The primordial $^4$He abundance (Y$_p$) is one of the key characteristics of
Primordial Nucleosynthesis processes that occurred in the first minutes after
the Big Bang. Its value depends on the baryon/photon ratio $\eta\equiv
n_b/n_{\gamma}$, and is also sensitive to the relativistic degrees of freedom
which affect the expansion rate of the Universe at the radiation-dominated era.
The most used method of the determination of Y$_p$ is the study of the metal
deficient HII regions located in blue compact dwarf galaxies (BCDs). In this
paper, we discuss in detail various methods of the determination of HII region
metallicity in the context of Y$_p$ analyses. We show that some procedures used
in the methods lead to biases in the metallicity estimates and underestimation
of their uncertainties. We propose a modified method for the metallicity
determination, as well as an additional criterion for selecting objects. We
have selected 69 objects (26 objects with high quality spectra from the
HeBCD+NIR database and 43 objects from the SDSS catalog), for which we estimate
Y and O/H using the proposed method. We have estimated Y$_p=0.2470\pm0.0020$
which is one of the most accurate estimates obtained up to date. Its comparison
with the value Y$_p=0.2470\pm0.0002$ obtained as a result of numerical
modelling of Primordial Nucleosynthesis with the value of $\Omega_b$ taken from
the analysis of the CMB anisotropy (Planck mission), is an important tool for
studying the self-consistency of the Standard cosmological model (a possible
discrepancy between these estimates could be an indicator of a new physics).
The application of the proposed method allows one to more correctly estimate
Y$_p$ and the slope $d$Y/$d$(O/H). Further analysis of the data from the SDSS
catalog can significantly increase the statistics of objects for the regression
analysis, which in turn can refine the Y$_p$ estimate.
