Likelihood-ratio test statistic for the finite-sample case in nonlinear ordinary differential equation models
Fig 9
Data-space representation of four different scenarios using the nodal curve model manifold example.
(A,D,G,J) Different shapes of the model manifold (black solid line) in the data space with a choice of data realisations (N = 25 out of 200, gray crosses) drawn from a n-ball around the true parameter (blue cross) and fit onto the model manifold (gray solid line and red circles). Distances between the true parameter and the fits (N = 200) correspond to the empirical likelihood ratio. (B,E,H,K) Corresponding histograms to each scenario illustrate the distribution of the distances, i.e. likelihood ratios compared to a -distribution (red line). (C,F,I,L) The pp-plot panel allows for a detailed comparison of the empirical likelihood ratios to a
-distribution (N = 200).