  In this paper, we develop new test statistics for private hypothesis testing.
These statistics are designed specifically so that their asymptotic
distributions, after accounting for noise added for privacy concerns, match the
asymptotics of the classical (non-private) chi-square tests for testing if the
multinomial data parameters lie in lower dimensional manifolds (examples
include goodness of fit and independence testing). Empirically, these new test
statistics outperform prior work, which focused on noisy versions of existing
statistics.
