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. Baddeley et al. (2005) as an empirical counterpart of the Campbell equilibrium equation for marked Gibbs point processes. The present paper focuses on stationary marked Gibbs ...

We take a fresh look at Theil’s BLUS residuals and ask why they have gone out of fashion. All our simulation experiments indicate that tests based on BLUS residuals have higher power than those based on the more popular recursive residuals, even in those cases (structural breaks) where intuition would favour the recursive residuals. JEL Classification: B23; C10; C13; C20

In this study, the residuals in time series analysis, which were classified in four different classes as ”conditional residuals”, ”unconditional residuals”, ”innovation” and ”normalized residuals”, are calculated by a simulation study for the ARMA model under certain parameter values for different numbers of observation and their conditions in diagnostic checking are examined using the test sta...

Christensen and Lin (2014), henceforth C-L, suggested two lack-of-fit tests to assess the adequacy of a linear model based on partial sums of residuals. In particular, their tests evaluated the adequacy of the mean function. Their tests relied on asymptotic results without requiring small sample normality. We extend this research by proposing additional tests based on partial sums of residuals....

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order n−1, where n is the sample size. We define corrected Pearson residuals for these models that, to this order of approximation, have exactly the same distribution of the true Pearson residuals. Applic...

A theorem of Dolfi, Herzog, Kaplan, and Lev \cite[Thm.~C]{DHKL} asserts that in a finite group with trivial Fitting subgroup, the size soluble residual is bounded from below by certain power order, inequality sharp. Inspired this result some arguments \cite{DHKL}, we establish following generalisation: if $\mathfrak{X}$ subgroup-closed formation full characteristic which does not contain all gr...

Residuals in fault detection and diagnosis are usually designed with directional or structured properties to facilitate fault isolation. With directional residuals, best isolation is achieved if the residual directions are orthogonal. In the presence of noise, the residuals are subjected to statistical testing. Testing conditions are ideal if the Fisher information matrix of the residuals is di...