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The analysis of left truncated bivariate data using frailty models
Author(s) -
Wang Antai,
Chandra Krishnendu,
Jia Xieyang
Publication year - 2018
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12324
Subject(s) - bivariate analysis , mathematics , copula (linguistics) , goodness of fit , generalization , truncation (statistics) , econometrics , bivariate data , compositional data , statistics , mathematical analysis
In this paper, we study the properties of frailty models for bivariate data under fixed left truncation. It turns out that the distribution of completely observable pairs is also a member of the Archimedean copula family. We propose a new estimation strategy to analyze this type of data using the corresponding Kendall distribution. A general goodness‐of‐fit test procedure is then developed for selecting the best model. Our strategies are generalization of the methodologies proposed for left truncated data. We demonstrate our new approaches using simulations and an illustrative example and end our paper with some discussion.