Estimation from cross-sectional data under a semiparametric truncation model

Author:

Heuchenne C1,De Uña-Álvarez J2,Laurent G1

Affiliation:

1. HEC Management School, University of Liège, rue Louvrex 14, 4000 Liège, Belgium

2. Department of Statistics and Operations Research, University of Vigo, 36310 Vigo, Spain

Abstract

Summary Cross-sectional sampling is often used when investigating inter-event times, resulting in left-truncated and right-censored data. In this paper, we consider a semiparametric truncation model in which the truncating variable is assumed to belong to a certain parametric family. We examine two methods of estimating both the truncation and the lifetime distributions. We obtain asymptotic representations of the estimators for the lifetime distribution and establish their weak convergence. Both of the proposed estimators perform better than Wang’s (1991) nonparametric maximum likelihood estimator in terms of the integrated mean squared error, when the parametric family for the truncation is sufficiently close to its true distribution. The full likelihood approach is preferable to the conditional likelihood approach in estimating the lifetime distribution, though not necessarily the truncation distribution. In an application to Alzheimer’s disease data, hypothesis tests reject the uniform truncation distribution, but several other parametric models lead to similar behaviour of the truncation and lifetime distributions after disease onset.

Funder

Spanish Ministerio de Economía y Competitividad

European Regional Development Fund

Belgian Fund for Scientific Research

Louvain School of Statistics

Biomedical Research Centre at Vigo University

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Statistics, Probability and Uncertainty,General Agricultural and Biological Sciences,Agricultural and Biological Sciences (miscellaneous),General Mathematics,Statistics and Probability

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Estimation for the Cox model with biased sampling data via risk set sampling;Journal of Statistical Planning and Inference;2024-01

2. Nonparametric Entropy Estimation of Conditional Distribution Under Length-Biased Right Censored Sample;Journal of Statistical Theory and Practice;2023-02-27

3. One‐Sample Problems;The Statistical Analysis of Doubly Truncated Data;2022-01-14

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