We present two methods for regression transformation diagnostics in the transform-both-sides model (see Carrol and Ruppert, 1984, 1987; Hinkley and Wang, 1988). One is based on the likelihood displacement proposed by Cook and Weisberg (1982) for assessing the influence of individual cases on the...

A preferred point [alpha]-geometry is introduced in this note, which is a natural extension of the work of Critchley et al. (1993, 1994). Using this geometry, the homogeneous structure and the duality are discussed. We also define a new [alpha]-divergence function and produce a flatness...

Least absolute deviations (LAD) regression, i.e. L1 regression, is more resistant to the outliers in the response variable than the least-squares regression, but is relatively sensitive to outlying observations in explanatory variables. However, some but few attentions have been contributed to...

We consider a new mathematical object called preferred point [alpha]-manifold, which is a natural extension of Lauritzen (1987) and Critchley et al. (1993). A sufficient and necessary condition is given to guarantee that preferred point [alpha]-geometry subsumes a statistical manifold. We...

Regression model with skew-normal errors provides useful extension for ordinary normal regression models when the data set under consideration involves asymmetric outcomes. On the other hand, the homogeneity of variances (if they exist) is a standard assumption in skew-normal nonlinear...

We extend some diagnostic methods studied by Pregibon (1981, Ann. Statist. 9, 705-724), Cook and Weisberg (1982, Residuals and Influence in Regression, Chapman & Hall, New York), and Wei (1998, Exponential Family Nonlinear Models, Springer, Singapore) to nonlinear reproductive dispersion models...