Nonparametric Methods for Doubly Truncated Data
1999; Volume: 94; Issue: 447 Linguagem: Inglês
10.1080/01621459.1999.10474187
ISSN1537-274X
Autores Tópico(s)Advanced Statistical Methods and Models
ResumoAbstract Truncated data play an important role in the statistical analysis of astronomical observations as well as in survival analysis. The motivating example for this article concerns a set of measurements on quasars in which there is double truncation. That is, the quasars are observed only if their luminosity occurs within a certain finite interval, bounded at both ends, with the interval varying for different observations. Nonparametric methods for the testing and estimation of doubly truncated data are developed. These methods extend some known techniques for data that are truncated only on one side, in particular Lynden-Bell's estimator and the truncated version of Kendall's tau statistic. However the kind of hazard function arguments that underlie the one-sided methods fail for two-sided truncation. Bootstrap and Markov Chain Monte Carlo techniques are used here in their place. Finally, we apply these techniques to the quasar data, answering a question about their long-term luminosity evolution. Key Words: BootstrapHypothesis testLuminosity evolutionLynden-Bell estimatorMarkov chain Monte CarloQuasarsSelf-consistencyTau test
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