  A necessary and suffcient condition for Pitman's asymptotic relative
effciency (ARE) of the Kendall and Spearman correlation statistics for the
independence test to be 1 is given, in terms of certain smoothness and
nondegeneracy properties of the model. Corresponding easy to use and broadly
applicable sufficient conditions are obtained, which are then illustrated on
several known models of dependence. Effects of the presence or absence of the
smoothness and/or nondegeneracy parts of the mentioned necessary and suffcient
condition are demonstrated using certain specially constructed dependence
models. A more general (than usual) version of Pitman's ARE is developed, with
broader and easier to check conditions of applicability. This version of the
ARE, which is then used in the rest of the paper, may also be of value
elsewhere.
