  We introduce new consistent and scale-free goodness-of-fit tests for the
exponential distribution based on Puri-Rubin characterization. For the
construction of test statistics we employ weighted $L^2$ distance between
$V$-empirical Laplace transforms of random variables that appear in the
characterization. The resulting test statistics are degenerate V-statistics
with estimated parameters. We compare our tests, in terms of the Bahadur
efficiency, to the likelihood ratio test, as well as some recent
characterization based goodness-of-fit tests for the exponential distribution.
We also compare the powers of our tests to the powers of some recent and
classical exponentiality tests. In both criteria, our tests are shown to be
strong and outperform most of their competitors.
