  We introduce the "partial-$p$" operation in a massive Euclidean
$\lambda\phi^{4}$ scalar field theory describing anisotropic Lifshitz critical
behavior. We then develop a minimal subtraction a la
$Bogoliubov-Parasyuk-Hepp-Zimmermann$ renormalization scheme. As an application
we compute critical exponents diagrammatically using the orthogonal
approximation at least up to two-loop order and show their equivalence with
other renormalization techniques. We discuss possible applications of the
method in other field-theoretic contexts.
