  The \delta N formalism is extended to include the perturbation of the vector
field. The latter is quantized in de Sitter space-time and it is found that in
general the particle production process of the vector field is anisotropic.
This anisotropy is parametrized by introducing two parameters p and q, which
are determined by the conformal invariance breaking mechanism. If any of them
are non-zero, generated \zeta is statistically anisotropic. Then the power
spectrum of \zeta and the non-linearity parameter fNL have an angular
modulation. This formalism is applied for two vector curvaton models and the
end-of-inflation scenario. It is found that for p \ne 0, the magnitude of fNL
and the direction of its angular modulation is correlated with the anisotropy
in the spectrum. If p \gtrsim 1, the anisotropic part of fNL is dominant over
the isotropic one. These are distinct observational signatures; their detection
would be a smoking gun for a vector field contribution to \zeta . In the first
curvaton model the vector field is non-minimally coupled to gravity and in the
second one it has a time varying kinetic function and mass. In the former, only
statistically anisotropic \zeta can be generated, while in the latter,
isotropic \zeta may be realized too. Parameter spaces for these vector curvaton
scenarios are large enough for them to be realized in the particle physics
models. In the end-of-inflation scenario fNL have similar properties to the
vector curvaton scenario with additional anisotropic term.
