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. Author manuscript; available in PMC: 2017 Mar 1.
Published in final edited form as: J Am Stat Assoc. 2016 May 5;111(513):107–117. doi: 10.1080/01621459.2015.1123157

Figure 1.

Figure 1

Geometric interpretation of the problem. The true distribution function P0(Y|X) for Y given (X, Z) across all values of β is depicted in the left panel, with the true value of β, i.e., β0 shown. In the right top panel, we see the true distribution function P0(Y|X) for Y given X across all values of β with β0 shown. The assumed external data model is given in the bottom right panel across all values of θ, with the solution θ* to (1) being shown as the minimizer of the Kullback-Leibler distance between the fixed P0(Y|X) and the model space of gθ(Y|X).