Very often statistical data contain heterogeneous types of outcome variables which come from the same experimental unit. For analyzing such data, one usually considers marginal and correlation models and applies a quasi-likelihood approach which works well in the large sample case. Although simulation studies are necessary for investigating small-sample performance, no systematic procedure has been available for generating heterogeneous types of dependent variables under such partially specified form of distributional models. An appealing procedure is proposed here that works for broad classes of distributions under nonnegative correlation structures. This procedure has been designed for higher-dimensional vectors of infinitely divisible component variables, but the basic idea is applicable to a more general distributional setup in the bivariate case. The proposed approach is illustrated with several graphical presentations of simulated data.

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Keywords Correlation structure, Heterogeneous variables, Infinitely divisible distributions, Quasi-likelihood, Random vector generation
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Journal Computational Statistics and Data Analysis
Park, C. (2004). Construction of random vectors of heterogeneous component variables under specified correlation structures. Computational Statistics and Data Analysis, 46(4), 621–630. doi:10.1016/j.csda.2003.10.010