The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gauss...

The error distribution testing plays an important role in linear regression as misspecification seriously affects the validity and efficiency of analysis. least squares (OLS) residuals are often used to construct test statistics; order overcome non-independent identically residuals, best unbiased scale (BLUS) applied this paper, which, unlike OLS vector is independently distributed. Based on BL...

By means of a series of borehole resistivity measurements and a resistivity±salinity relation, a particular salt-freshwater inversion was found under the shore with semi-diurnal tides at the French±Belgian border. These resistivity data provide valuable information about the vertical variation of the saltwater percentage in di€erent boreholes. At di€erent places and depths ̄uctuations of freshwa...

Friedman’s super smoother is a nonparametric regression estimator based on local linear regression with adaptive bandwidths (Friedman [1984]). The basic idea is to first estimate a number of fixed bandwidth smooths by local linear regression. The leave-one-out cross-validated residuals from each of those initial estimates are then smoothed using a constant bandwidth. Based on the smoothed resid...

This paper applies a recently developed optimization method to examine the design of networks that monitor radiation under routine conditions. Annual gamma dose rates were modelled by combining regression with interpolation of the regression residuals using spatially exhaustive predictors and an anisotropic variogram of the residuals. Locations of monitoring stations were optimized by minimizin...

This the problem maximum asymptotic bias of regression estimates over a-contamination for the joint of the response carriers. Two classes of estimates are treated: (1) Msestimates with bounded function p applied to the scaled residuals, using a very general class of scale estimates, and (2) Bounded influence function type generalized M-estimates. Estimates in the first class are oblta1rled as p...

Generalized estimating equations (GEE) fit parameters based on sums of weighted residuals, which may be applied for example to the Poisson distribution. We discuss Generalized Poisson (GP) response data. This distribution has a more flexible variance function than the Poisson distribution and has an additional dispersion parameter. To fit this parameter, second level estimating equations based ...

‘Classical regression analysis’ assumes the normality (N), homoscedasticity (H) and serial independence (I) of regression residuals. Violation of the normality assumption may lead the investigator to inaccurate inferential statements. Recently, tests for normality have been derived for the case of homoscedastic serially independent (HZ) residuals [e.g., White and Macdonald (1980)]. Similarly, t...