Asymptotic properties of plug-in level set estimators for right censored data

作者：Wang YangFeng; Yang Ying^*

来源：Science China Mathematics, 2014, 57(6): 1257-1274.

DOI：10.1007/s11425-013-4727-5

• level set
• asymptotic normality
• highest density region
• convergence rate
• right censored data

We assume T (1), aEuro broken vertical bar, T (n) are i.i.d. data sampled from distribution function F with density function f and C (1), aEuro broken vertical bar, C (n) are i.i.d. data sampled from distribution function G. Observed data consists of pairs (X (i) , delta (i) ), i = 1, aEuro broken vertical bar, n, where X (i) = min{T (i) ,C (i) }, delta (i) = I(T (i) a (c) 1/2 C (i) ), I(A) denotes the indicator function of the set A. Based on the right censored data {X (i) , delta (i) }, i = 1, aEuro broken vertical bar,n, we consider the problem of estimating the level set {f a (c) 3/4 c} of an unknown one-dimensional density function f and study the asymptotic behavior of the plug-in level set estimators. Under some regularity conditions, we establish the asymptotic normality and the exact convergence rate of the lambda (g) -measure of the symmetric difference between the level set {f a (c) 3/4 c} and its plug-in estimator {fn a (c) 3/4 c}, where f is the density function of F, and f (n) is a kernel-type density estimator of f. Simulation studies demonstrate that the proposed method is feasible. Illustration with a real data example is also provided.

• 出版日期2014-6
• 单位清华大学