  We consider the benefits of measuring cosmic statistical anisotropy from
redshift-space correlators of the galaxy number density fluctuation and the
peculiar velocity field without adopting the plane-parallel (PP) approximation.
Since the correlators are decomposed using the general tripolar spherical
harmonic (TripoSH) basis, we can deal with wide-angle contributions untreatable
by the PP approximation, and at the same time, target anisotropic signatures
can be cleanly extracted. We, for the first time, compute the covariance of the
TripoSH decomposition coefficient and the Fisher matrix to forecast the
detectability of statistical anisotropy. The resultant expression of the
covariance is free from nontrivial mixings between each multipole moment caused
by the PP approximation and hence the detectability is fully optimized.
Compared with the analysis under the PP approximation, the superiority in
detectability is always confirmed, and it is highlighted, especially in the
cases that the shot noise level is large and that target statistical anisotropy
has a blue-tilted shape in Fourier space. The application of the TripoSH-based
analysis to forthcoming all-sky survey data could result in constraints on
anisotropy comparable to or tighter than the current cosmic microwave
background ones.
