Author/Authors :
Kheyri, Azam Department of Statistics - Ordered and Spatial Data Center of Excellence - Ferdowsi University of Mashhad, Mashhad, Iran , Amini, Mohammad Department of Statistics - Ordered and Spatial Data Center of Excellence - Ferdowsi University of Mashhad, Mashhad, Iran , Jabbari, Hadi Department of Statistics - Ordered and Spatial Data Center of Excellence - Ferdowsi University of Mashhad, Mashhad, Iran , Bozorgnia, Abolghasem Department of Statistics - Khayyam University, Mashhad, Iran
Abstract :
In this paper, the kernel distribution function estimator for negative super-
additive dependent (NSD) random variables is studied. The exponential inequalities
and exponential rate for the kernel estimator are investigated. Under certain regularity
conditions, the optimal bandwidth is determined using the mean squared error and
is found to be the same as that in the independent identically distributed case. A
simulation study to examine the behavior of the kernel and empirical estimators is
given. Moreover, a real data set in hydrology is analyzed to demonstrate the structure
of negative superadditive dependence, and as a result, the kernel distribution function
estimator of the data is investigated.
