Suppose that we observe bivariate data (Xi, Yi) only when Yi [less-than-or-equals, slant] Xi (left truncation). Denote with F the marginal d.f. of the X's. In this paper we derive a Bahadur-type representation for the quantile function of the pertaining product-limit estimator of F. As an...

In random truncation models one observes the i.i.d. pairs (Ti[less-than-or-equals, slant]Yi),i=1, ..., n. IfYis the variable of interest, thenTis another independent variable which prevents the complete observation ofYand random left truncation occurs. Such a type of incomplete data is...

In this study bivariate kernel density estimators are considered when a component is subject to random truncation. In bivariate truncation models one observes the i.i.d. samples from the triplets (T, Y, X) only if T[less-than-or-equals, slant]Y. In this set-up, Y is said to be left...