Page - 333 - in Differential Geometrical Theory of Statistics

Entropy2016,18, 421 (a) (+1)−affine parameters ξ1 ξ2 (b) (−1)−affine parameters π1 0.0 0.2 0.4 0.6 0.8 1.0 Figure1. Level sets ofK(π0,π), forfixedπ0 = (16, 2 6, 3 6) in: (a) thenaturalparameters, and (b) the meanparameters. (a) (+1)−affine parameters ξ1 ξ2 (b) (−1)−affine parameters π1 0.0 0.2 0.4 0.6 0.8 1.0 Figure2. Level setsofK∗(π0,π), forfixedπ0=(16, 2 6, 3 6) in: (a) thenaturalparameters, and (b) the meanparameters. 4. SimulationStudies In this section,weundertakesimulationstudies tonumericallyexplorewhathasbeendiscussed above. Separatesub-sectionsaddress threegeneral topics—focusingononeparticular instanceofeach, as follows: 1. The transition as (N,k) varies between discrete and continuous features of the sampling distributions of goodness-of-fit statistics—focusing on the behaviour of the deviance at the uniformdiscretedistribution; 2. ThecomparativebehaviourofarangeofPower-Divergencestatistics—focusingontherelative stabilityof their samplingdistributionsnear theboundary; 3. The lackofuniformity—across theparameterspace—of thefinitesampleadequacyofstandard asymptotic samplingdistributions, focusingontesting independence in2×2contingencytables. 333