 Proposal-budget variance comparison of importance and rejection sampling

At equal proposal count, compare $\int {\varphi }^2{f}^2/g-{\theta }^2$ for unnormalized importance sampling with $M(\int {\varphi }^{2}f-{\theta }^2)$ for the accepted-sample mean. There is no universal ordering for nonzero target mean. For zero mean, the bounded-weight inequality gives importance sampling no larger asymptotic variance. Empty rejected samples and per-proposal computational cost are separate considerations.