Abstract
Many statistical methods for truncated data rely on the independence assumption regarding the truncation variable. In many application studies, however, the dependence between a variable X of interest and its truncation variable L plays a fundamental role in modeling data structure. For truncated data, typical interest is in estimating the marginal distributions of (L, X) and often in examining the degree of the dependence between X and L. To relax the independence assumption, we present a method of fitting a parametric model on (L, X), which can easily incorporate the dependence structure on the truncation mechanisms. Focusing on a specific example for the bivariate normal distribution, the score equations and Fisher information matrix are provided. A robust procedure based on the bivariate t-distribution is also considered. Simulations are performed to examine finite-sample performances of the proposed method. Extension of the proposed method to doubly truncated data is briefly discussed.
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An erratum to this article is available at http://dx.doi.org/10.1007/s00362-014-0626-2.
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Emura, T., Konno, Y. Multivariate normal distribution approaches for dependently truncated data. Stat Papers 53, 133–149 (2012). https://doi.org/10.1007/s00362-010-0321-x
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DOI: https://doi.org/10.1007/s00362-010-0321-x
Keywords
- Correlation coefficient
- Truncation
- Maximum likelihood
- Missing data
- Multivariate analysis
- Parametric bootstrap