  We conduct a comprehensive study on dropout galaxy candidates at $z\sim9-16$
using the first 90 arcmin$^2$ JWST/NIRCam images taken by the early release
observations (ERO) and early release science (ERS) programs. With the JWST
simulation images, we find that a number of foreground interlopers are selected
with a weak photo-$z$ determination ($\Delta\chi^2>4$). We thus carefully apply
a secure photo-$z$ selection criterion ($\Delta\chi^2>9$) and conventional
color criteria with confirmations of the ERO NIRSpec spectroscopic redshifts,
and obtain a total of 23 dropout galaxies at $z\sim9-16$, including two
candidates at $z_\mathrm{phot}=16.25_{-0.46}^{+0.24}$ and
$16.41_{-0.55}^{+0.66}$. We perform thorough comparisons of dropout galaxies
found in our work with recent JWST studies, and conclude that our galaxy sample
is reliable enough for statistical analyses. We derive the UV luminosity
functions at $z\sim9-16$, and confirm that our UV luminosity functions at
$z\sim 9$ and $12$ agree with those determined by other HST and JWST studies.
The cosmic star-formation rate density decreases from $z\sim9$ to $12$, and
perhaps to $16$, but the densities at $z\sim12-16$ are higher than the constant
star formation efficiency model. Interestingly, there are six bright galaxy
candidates at $z\sim10-16$ with $M_\mathrm{UV}<-19.5$ mag and $M_*\sim10^{8-9}
M_\odot$. Because a majority ($\sim80$\%) of these galaxies show no signatures
of AGNs in their morphologies, the high cosmic star-formation rate densities
and the existence of these UV-luminous galaxies are explained by no suppression
of star-formation by the UV background radiation at the pre-reionization epoch
and/or an efficient UV radiation production by a top-heavy IMF with Population
III-like star formation.
