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Robustness in Latent Variable Models

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Figure 2.1: Figures (a)–(b) illustrate Example 2.1, plots of βNassumed model0(σU) and β1(σU) for N(τ (a), τ (a)) and three true X distributions, N(1, 1) (solid line),(0·5, 1) (dashed line) and N(1·5, 1) (dashed-dotted line); (c)–(d) single-sample re-measurement versions of (a)–(b) as described in Example 4.1.
Figure 2.2: Plots for Example 2.2 with Y |X linear-probit. (a)–(b), θ(n)(σU)−θ(m)(σU)and θ(s)(σU) − θ(m)(σU); (c)–(d) Monte-Carlo estimates based on 100 replicates, offinite-sample, n = 500, version of (a)–(b)
Table 4.1: Values of Testimates whenused in Example 4.2. Corresponding ∗1,1 and T ∗1,2 assessing robustness of the regression parameter λ = 0 and λ = 3 under three ways of modeling for the simulated data p-values are given in the parentheses.
Figure 4.1: Deviations from the MLEs resulting from the mixture-normal modeling �
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