scholarly journals A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring

2001 ◽  
Vol 79 (1) ◽  
pp. 138-155 ◽  
Author(s):  
Louis-Paul Rivest ◽  
Martin T. Wells
Keyword(s):  
Survival Function ◽  
Dependent Censoring ◽  
Martingale Approach

Survival forests for data with dependent censoring

2017 ◽  
Vol 28 (2) ◽  
pp. 445-461 ◽  
Author(s):  
Hoora Moradian ◽  
Denis Larocque ◽  
François Bellavance
Keyword(s):  
Survival Data ◽  
Survival Function ◽  
Real Data ◽  
Dependent Censoring ◽  
Right Censoring ◽  
True Time ◽  
Splitting Rule ◽  
The Individual ◽  
Individual Trees ◽  
Survival Forests

Tree-based methods are very powerful and popular tools for analysing survival data with right-censoring. The existing methods assume that the true time-to-event and the censoring times are independent given the covariates. We propose different ways to build survival forests when dependent censoring is suspected, by using an appropriate estimator of the survival function when aggregating the individual trees and/or by modifying the splitting rule. The appropriate estimator used in this paper is the copula-graphic estimator. We also propose a new method for building survival forests, called p-forest, that may be used not only when dependent censoring is suspected, but also as a new survival forest method in general. The results from a simulation study indicate that these modifications improve greatly the estimation of the survival function in situations of dependent censoring. A real data example illustrates how the proposed methods can be used to perform a sensitivity analysis.

Estimating the survival function based on the semi-Markov model for dependent censoring

2015 ◽  
Vol 22 (2) ◽  
pp. 161-190
Author(s):  
Ziqiang Zhao ◽  
Ming Zheng ◽  
Zhezhen Jin
Keyword(s):  
Markov Model ◽  
Survival Function ◽  
Dependent Censoring

Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

2020 ◽  
Vol 72 (2) ◽  
pp. 111-121
Author(s):  
Abdurakhim Akhmedovich Abdushukurov ◽  
Rustamjon Sobitkhonovich Muradov
Keyword(s):  
Relative Risk ◽  
Sample Size ◽  
Censored Data ◽  
Survival Function ◽  
Survival Functions ◽  
Power Structures ◽  
Bivariate Survival ◽  
Empirical Estimates ◽  
Bivariate Survival Function ◽  
Product Limit

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01

scholarly journals A Unified Formulation of k-Means, Fuzzy c-Means and Gaussian Mixture Model by the Kolmogorov–Nagumo Average

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 518
Author(s):  
Osamu Komori ◽  
Shinto Eguchi
Keyword(s):  
Pareto Distribution ◽  
Statistical Data ◽  
Learning Algorithm ◽  
Survival Function ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Simulation Studies ◽  
Probabilistic Framework ◽  
Underlying Distribution ◽  
Fuzzy C Means

Clustering is a major unsupervised learning algorithm and is widely applied in data mining and statistical data analyses. Typical examples include k-means, fuzzy c-means, and Gaussian mixture models, which are categorized into hard, soft, and model-based clusterings, respectively. We propose a new clustering, called Pareto clustering, based on the Kolmogorov–Nagumo average, which is defined by a survival function of the Pareto distribution. The proposed algorithm incorporates all the aforementioned clusterings plus maximum-entropy clustering. We introduce a probabilistic framework for the proposed method, in which the underlying distribution to give consistency is discussed. We build the minorize-maximization algorithm to estimate the parameters in Pareto clustering. We compare the performance with existing methods in simulation studies and in benchmark dataset analyses to demonstrate its highly practical utilities.

scholarly journals The Stability of the Aggregate Loss Distribution

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 91 ◽  
Author(s):  
Riccardo Gatto
Keyword(s):  
Stability Analysis ◽  
Survival Function ◽  
Saddlepoint Approximation ◽  
Computational Formula ◽  
Important Indicator ◽  
The Common ◽  
Infinitesimal Perturbation ◽  
Aggregate Loss ◽  
Aggregate Loss Distribution ◽  
The Stability

In this article we introduce the stability analysis of a compound sum: it consists of computing the standardized variation of the survival function of the sum resulting from an infinitesimal perturbation of the common distribution of the summands. Stability analysis is complementary to the classical sensitivity analysis, which consists of computing the derivative of an important indicator of the model, with respect to a model parameter. We obtain a computational formula for this stability from the saddlepoint approximation. We apply the formula to the compound Poisson insurer loss with gamma individual claim amounts and to the compound geometric loss with Weibull individual claim amounts.

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