scholarly journals General Bootstrap for Dual ϕ-Divergence Estimates

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Salim Bouzebda ◽  
Mohamed Cherfi
Keyword(s):  
Coverage Probability ◽  
Empirical Process ◽  
Asymptotic Properties ◽  
Process Theory ◽  
General Notion ◽  
Finite Sample ◽  
Confidence Set ◽  
Empirical Process Theory ◽  
Divergence Estimates ◽  
Simulation Results

A general notion of bootstrappedϕ-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrappedϕ-divergence estimates are obtained, by means of the empirical process theory, which are applied to construct the bootstrap confidence set with asymptotically correct coverage probability. Some of practical problems are discussed, including, in particular, the choice of escort parameter, and several examples of divergences are investigated. Simulation results are provided to illustrate the finite sample performance of the proposed estimators.

scholarly journals Gradient and Likelihood Ratio Tests in Cure Rate Models

2016 ◽  
Vol 5 (4) ◽  
pp. 9 ◽  
Author(s):  
Hérica P. A. Carneiro ◽  
Dione M. Valença
Keyword(s):  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Information Matrix ◽  
Survival Models ◽  
Finite Sample ◽  
Cure Rate ◽  
Time Model ◽  
Cure Rate Models ◽  
Large Sample ◽  
Finite Samples

In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently  a new test called \textit{gradient test} has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we  performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results.

scholarly journals Heterogeneous individual risk modelling of recurrent events

Biometrika ◽  
2020 ◽  
Author(s):  
Huijuan Ma ◽  
Limin Peng ◽  
Chiung-Yu Huang ◽  
Haoda Fu
Keyword(s):  
Recurrent Events ◽  
Asymptotic Properties ◽  
Dynamic Modelling ◽  
Individual Risk ◽  
Simulation Studies ◽  
Finite Sample ◽  
Risk Modelling ◽  
Modelling Framework ◽  
Proposed Model

Summary Progression of chronic disease is often manifested by repeated occurrences of disease-related events over time. Delineating the heterogeneity in the risk of such recurrent events can provide valuable scientific insight for guiding customized disease management. We propose a new sensible measure of individual risk of recurrent events and present a dynamic modelling framework thereof, which accounts for both observed covariates and unobservable frailty. The proposed modelling requires no distributional specification of the unobservable frailty, while permitting exploration of the dynamic effects of the observed covariates. We develop estimation and inference procedures for the proposed model through a novel adaptation of the principle of conditional score. The asymptotic properties of the proposed estimator, including the uniform consistency and weak convergence, are established. Extensive simulation studies demonstrate satisfactory finite-sample performance of the proposed method. We illustrate the practical utility of the new method via an application to a diabetes clinical trial that explores the risk patterns of hypoglycemia in type 2 diabetes patients.

Learning Block Structures in U-statistic Based Matrices

Biometrika ◽  
2020 ◽  
Author(s):  
Weiping Zhang ◽  
Baisuo Jin ◽  
Zhidong Bai
Keyword(s):  
Matrix Theory ◽  
Block Structure ◽  
Group Structure ◽  
Asymptotic Properties ◽  
Finite Sample ◽  
Eigenvalues And Eigenvectors ◽  
Sample Matrix ◽  
U Statistics ◽  
Large Matrix ◽  
Block Structures

Abstract We introduce a conceptually simple, efficient and easily implemented approach for learning the block structure in a large matrix. Using the properties of U-statistics and large dimensional random matrix theory, the group structure of many variables can be directly identified based on the eigenvalues and eigenvectors of the scaled sample matrix. We also established the asymptotic properties of the proposed approach under mild conditions. The finite-sample performance of the approach is examined by extensive simulations and data examples.

scholarly journals Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 394-417
Author(s):  
Aboubacrène Ag Ahmad ◽  
El Hadji Deme ◽  
Aliou Diop ◽  
Stéphane Girard
Keyword(s):  
Asymptotic Properties ◽  
Real Data ◽  
Scale Model ◽  
Extreme Value Index ◽  
Finite Sample ◽  
Scale Functions ◽  
Nonparametric Estimators ◽  
Heavy Tailed Distributions ◽  
Finite Sample Properties ◽  
Heavy Tailed

AbstractWe introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

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