How to calculate the goodness-of-fit of a fractal dimension To the Editor, Karyometric data are helpful for differential diagnosis and prognosis [1–4]. A new morphometric variable, the coefficient of determination of the Minkowski frac-tal dimensions (the R 2 value between the y of the regression lines and y values of the real data) has recently been introduced [1,2]. Adam et al. [1] described ...

Results of a simulation study of the fit of data to an estimated parametric model are reported. Three particular models including the two-parameter normal and exponential distributions, and the simple linear regression model are considered. A number of scaled versions of the least squares residuals from the regression model, and quantities that may be called residuals from the other two models ...

The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute residuals. A useful representation of the last problem is given to examine properties of the objective function and estimate the number of its local minima. It is sho...

Time series linear regression model with the stationary residuals has been studied in many fields, and well established. However, the stationary assumption on the residuals seems to be restrictive. Therefore, we extend the model to the case when the residuals are locally stationary. The best linear unbiased estimator (BLUE) of coefficient vector contains the residual covariance matrix which is ...

A common practice is to get reliable regression results in the generalized linear model which detection of influential cases. For identification cases, present study focuses compare empirically performance various existing residuals for case Poisson model. Furthermore, we computed Cook’s distance stated residuals. In order show effectiveness proposed methodology, data have been generated by usi...

We show that the power of the KPSS-test against integration, as measured by divergence rates of the test statistic under the alternative, remains the same when residuals from an OLS-regression rather than true observations are used. This is in stark contrast to residual based tests of the null of integration in a cointegration setting, where power is drastically reduced when residuals are used....

The Hinich (1982) bispectrum test for nonlinearity and Gaussianity indicates that the residuals of the Tiao-Box (1981) constrained and unconstrained VAR models for the gas furnace data reject the assumption of Gaussianity and linearity over a grid of bandwidths for estimating the bispectrum. These findings call into question the specification of the linear VAR and VARMA models assumed by Tiao-B...