Statistical Estimation Based on Interval Censored Data

Abstract

Abstract: Let Z₁, Z₂, …, Z_n be independent and identically distributed (iid) random variables (rv) with unknown distribution function F(x): U₁, U₂,…, U_n be iid rv, independent of X_i, 1 ≤ i ≤ n, with unknown distribution function G(x). We observe a sequence of identically distributed pairs U⁽ⁿ⁾ = (Ui,Wi), i = 1,2,…,n, where W _x = I(Z _x < X _x ) is the indicator of the event Z_i < X_i and (U_i.X_i) have joint density g(u,x). The problem of estimating the distribution function F(x) and its quantile of the order λ based on sample U⁽ⁿ⁾ is considered. The asymptotic behavior of the constructed estimators is discussed.