  Jittering estimators are nonparametric function estimators for mixed data.
They extend arbitrary estimators from the continuous setting by adding random
noise to discrete variables. We give an in-depth analysis of the jittering
kernel density estimator, which reveals several appealing properties. The
estimator is strongly consistent, asymptotically normal, and unbiased for
discrete variables. It converges at minimax-optimal rates, which are
established as a by-product of our analysis. To understand the effect of adding
noise, we further study its asymptotic efficiency and finite sample bias in the
univariate discrete case. Simulations show that the estimator is competitive on
finite samples. The analysis suggests that similar properties can be expected
for other jittering estimators.
