Search results for "Correlation integral"
showing 3 items of 3 documents
Point process diagnostics based on weighted second-order statistics and their asymptotic properties
2008
A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex point process model with an arbitrary conditional intensity function, rather than a stationary Poisson model. Asymptotic properties of these generalized second-order statistics are derived, using an approach based on martingale theory.
A Note on Resampling the Integration Across the Correlation Integral with Alternative Ranges
2003
Abstract This paper reconsiders the nonlinearity test proposed by Ko[cbreve]enda (Ko[cbreve]enda, E. (2001). An alternative to the BDS test: integration across the correlation integral. Econometric Reviews20:337–351). When the analyzed series is non‐Gaussian, the empirical rejection rates can be much larger than the nominal size. In this context, the necessity of tabulating the empirical distribution of the statistic each time the test is computed is stressed. To that end, simple random permutation works reasonably well. This paper also shows, through Monte Carlo experiments, that Ko[cbreve]enda's test can be more powerful than the Brock et al. (Brock, W., Dechert, D., Scheickman, J., LeBar…
Local correlation functional for electrons in two dimensions
2008
We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation for the pair density. Then, we introduce an ad-hoc modification which better accounts for both the long-range correlation, and the kinetic-energy contribution to the correlation energy. The resulting functional is local, and depends parametrically on the number of electrons in the system. We apply this functional to the homogeneous electron gas and to a set of two-dimensional quantum dots covering a wide range of electron densities and thus various amount…