EFFECT OF ROUNDING ERRORS ON KERNEL DENSITY ESTIMATORS

In a model for rounded data suppose that the random sample X1,...,X(n), i.i.d., is transformed into an observed random sample X(1-DELTA),...,X(n-DELTA), where X(i-DELTA) = 2-nu-DELTA if X(i) is-an-element-of (2-nu-DELTA - DELTA, 2-nu-DELTA + DELTA), for i = 1,...,n. We show that the precision-DELTA of the observations has an important effect on the shape of the kernel density estimator, and we identify important points for the graphical display of this estimator. We examine the IMSE criteria to find the optimal window under the rounded-data model.