On finding interval estimates by the method of L. N. Bol'šev and E. A. Loginov

Let a random vector be observed with distribution function $F(x;\theta)$, parameter $\theta$ being unknown.
It is shown that the method of L. N. Bol'šev and E. A. Loginov [1] of finding interval estimates for a characteristic $\varphi(\theta)$ can be applied if $\varphi(\theta)$ and $F(x;\theta)$ are monotone in $\theta$.