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Nonparametric estimation for derivatives of compound distribution
Zhimin Zhang,Chaolin Liu 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.3
The compound random variableNj =1 Xj and its distribution have many applications in actuarial science. In this paper, we consider estimation of the derivative functionals of the compound distribution when the underlying density f of Xj is unknown. The estimator is constructed by Fourier inversion and kernel method. An order bound for the bias and asymptotic expression for the variance are given, and the asymptotic normality and uniform consistency are also discussed. Some simulation studies are presented to illustrate the performance of the estimator under finite sample setting.
Chao Lin,Xue-Song Sun,Sai-Lan Liu,Xiao-Yun Li,Nian Lu,Xin-Ling Li,Lin-Quan Tang,Ling Guo 대한암학회 2020 Cancer Research and Treatment Vol.52 No.3
Purpose The prognosis of nasopharyngeal carcinoma (NPC) patients with parotid lymph node (PLN) metastasis remains unclear. This study was performed to investigate the prognostic significance and optimal staging category of PLN metastasis and develop a nomogram for estimating individual risk. Materials and Methods Clinical data of 7,084 non-metastatic NPC patients were retrospectively reviewed. Overall survival (OS) was the primary endpoint. A nomogram was established based on the Cox proportional hazards regression model. The accuracy and calibration ability of this nomogram was evaluated by C-index and calibration curves with bootstrap validation. Results Totally, 164/7,084 NPC patients (2.3%) presented with PLNs. Multivariate analyses showed that PLN metastasis was a negative prognostic factor for OS, progression-free survival (PFS), distant metastasis-free survival (DMFS), and locoregional relapse-free survival (LRFS). Patients with PLN metastasis had a worse prognosis than N3 disease. Five independent prognostic factors were included in the nomogram, which showed a C-index of 0.743. The calibration curves for probability of 3- and 5-year OS indicated satisfactory agreement between nomogram-based prediction and actual observation. All results were confirmed in the validation cohort. Conclusion NPC patient with PLN metastasis had poorer survival outcome (OS, PFS, DMFS, and LRFS) than N3 disease. We developed a nomogram to provide individual prediction of OS for patients with PLN metastasis.