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Multivariate normal distribution approaches for dependently truncated data. (English) Zbl 1241.62094
Stat. Pap. 53, No. 1, 133-149 (2012); erratum ibid. 55, No. 4, 1233-1236 (2014).
Summary: 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 the 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.

MSC:
62H12 Estimation in multivariate analysis
62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62G10 Nonparametric hypothesis testing
62F40 Bootstrap, jackknife and other resampling methods
65C60 Computational problems in statistics (MSC2010)
Software:
bootstrap
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