Journal of the Iranian Statistical Society

Convergence Rate for Estimator of Distribution Function under NSD Assumption with an Application

Authors

1 Department of Statistics, Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Statistics, Khayyam University, Mashhad, Iran.

10.29252/jirss.18.2.21

Abstract

In this paper, the kernel distribution function estimator for negative superadditive 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.

Keywords

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Journal of the Iranian Statistical Society
Volume 18, Issue 2
December 2019
Pages 21-37
  • Receive Date: 23 July 2022
  • Revise Date: 13 May 2024
  • Accept Date: 23 July 2022