Residuals and goodness-of-fit tests for stationary marked Gibbs point processes

The inspection of residuals is a fundamental step to investigate the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed by Baddeley et al. (2005) as an empirical counterpart of the {\it Campbell equilibrium} equation for marked Gibbs point processes. The present paper focuses on stationary marked Gibbs point processes and deals with asymptotic properties of residuals for such processes. In particular, the consistency and the asymptotic normality are obtained for a wide class of residuals including the classical ones (raw residuals, inverse residuals, Pearson residuals). Based on these asymptotic results, we define goodness-of-fit tests with Type-I error theoretically controlled. One of these tests constitutes an extension of the quadrat counting test widely used to test the null hypothesis of a homogeneous Poisson point process

Skatole pattern during the growth period 50 to 100 kg liveweight in entire male pigs of the crossbreed combinations YDxLYD and HxLYD kept in groups of entire male pigs or in groups with dominant female pigs

1. Dominant females do not decrease the skatole and androstenone concentration in entire male pigs being dominated during the growth period from 50-100 kg liveweight (see fig. 1 and 3). 2. The amount of entire male pigs having higher skatole concentrations in blood – corresponding to skatole in backfat > 0.15 µg/g – are surprisingly high at 50 kg and 75 kg liveweight compared to 100 kg (10, 9 and 13 entire male pigs). 3. Furthermore it is not the same pigs having high skatole concentrations during the period from 50 over 75 to 100 kg liveweight. 4. The crossbreed HxLYD had significant higher skatole concentration in backfat at slaughter (100 kg liveweight) compared to the crossbreed YDxLYD (P<0.05)(see fig. 2). However, there was no significant difference in androstenone concentration in backfat at 100 kg liveweight between the 2 crossbreeds (see fig. 3)