FIGURE 4 |.

Four model configurations involving a bivariate generating process g(x₁, x₂) (in black), and two approximating models f₁(x₁, x₂) (in blue) and f₂(x₁, x₂) (in red). In all cases the approximating models are bivariate normal distributions whereas the generating process is a bivariate Laplace distribution. These model configurations are useful to explore changes in α′ (Equation 53), β′ (Equation 59) and $M_i^{\prime },W_{i^{\prime }},i=1,2$ (Equations 71, 72) as a function of sample size, as plotted in Figure 6. (A) g(x₁, x₂) is a bivariate Laplace distribution centered at 0 with high variance. All three models have means aligned along the 1: 1 line and marked with a black, blue, and red filled circle, respectively. Model f₁(x₁, x₂) is closest to the generating process. (B) Model f₁(x₁, x₂) is still the model closest to the generating process, at exactly the same distance as in (A) but misaligned from the 1: 1 line. (C) Here all three models are again aligned, but the generating process g(x₁, x₂) is an asymmetric bivariate Laplace that has a large mode at 0, 0 and smaller mode around the mean, marked with a black dot. In this case, the generating model is closer to model f₂(x₁, x₂) (in red). (D) Same as in (C), except model f₂(x₁, x₂) (in blue) is now misaligned, but still the closest model to the generating process.