  In Papers I-III, we use the flat-sky and distant-observer approximations to
develop a formalism with which the correlation statistics of cosmological
tensor fields are calculated by the nonlinear perturbation theory, generalizing
the integrated perturbation theory for scalar fields. In this work, the
formalism is extended to include the full-sky and wide-angle effects in
evaluating the power spectra and correlation functions of cosmological tensor
fields of any ranks. With the newly developed formalism, one can evaluate the
nonlinear power spectra and correlation functions to arbitrary higher orders in
principle. After describing the general formalism, we explicitly derive and
give analytic results of the lowest-order linear theory for an illustrative
purpose in this paper. The derived linear formulas with full-sky and wide-angle
effects are numerically compared with the previous formulas with flat-sky and
distant-observer limits in a simple model of tensor bias.
