Asymptotic expansion for ISE of kernel density estimators under censored dependent model

Fakoor, Vahid; Jomhoori, Sara; Azarnoosh, Hassan Ali

doi:10.1016/j.spl.2009.05.003

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2011

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“…2.11, we provide some asymptotic behaviors of kernel density estimation. The counterpart of these results for the censored dependent model was established by Fakoor et al (2009) andFakoor (2010). Some proofs of the results are deferred to the Appendix.…”

Section: Assumptionsmentioning

confidence: 84%

Some Asymptotic Results of Kernel Density Estimators Under Random Left-Truncation and Dependent Data

Fakoor¹,

Jomhoori²

2011

Communications in Statistics - Theory and Methods

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Problems with truncated data arise frequently in survival analyses and reliability applications. The estimation of the density function of the lifetimes is often of interest. In this article, the estimation of density function by the kernel method is considered, when truncated data are showing some kind of dependence. We apply the strong Gaussian approximation technique to study the strong uniform consistency for kernel estimators of the density function under a truncated dependent model. We also apply the strong approximation results to study the integrated square error properties of the kernel density estimators under the truncated dependent scheme.

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Section: Assumptionsmentioning

confidence: 84%