  Using the fact that some depth functions characterize certain family of
distribution functions, and under some mild conditions, distribution of the
depth is continuous, we have constructed several new multivariate goodness of
fit tests based on existing univariate GoF tests. Since exact computation of
depth is difficult, depth is computed with respect to a large random sample
drawn from the null distribution. It has been shown that test statistic based
on estimated depth is close to that based on true depth for a large random
sample from the null distribution. Some two sample tests for scale difference,
based on data depth are also discussed. These tests are distribution-free under
the null hypothesis. Finite sample properties of the tests are studied through
several numerical examples. A real data example is discussed to illustrate
usefulness of the proposed tests.
