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.
This article studies the estimation of the precision matrix of a high-dimensional Gaussian network. We investigate the graphical selector operator with shrinkage, GSOS for short, to maximize a penalized likelihood function where the elastic net-type penalty is considered as a combination of a norm-one penalty and a targeted Frobenius norm penalty. Numerical illustrations demonstrate that our proposed methodology is a competitive candidate for high-dimensional precision matrix estimation compared to some existing alternatives. We demonstrate the relevance and efficiency of GSOS using a foreign exchange markets dataset and estimate dependency networks for 32 different currencies from 2018 to 2021.
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