Fitting a Powered Exponential Autocorrelation: Alternatives to Maximum Likelihood via Conjugate Gradient Linear Solvers
Résumé
https://demonstrations.wolfram.com/FittingAPoweredExponentialAutocorrelationAlternativesToMaxim/.
Fitting a Powered Exponential Autocorrelation: Alternatives to Maximum Likelihood via Conjugate Gradient Linear Solvers.
The setting and the method are the same as in the Demonstration "Estimating a Centered Matérn (1) Process: Three Alternatives to Maximum Likelihood via Conjugate Gradient Linear Solvers",
except that the autocorrelation function, which was the Matérn function with differentiability-parameter $\nu$ equal to 1, is now replaced by the powered exponential autocorrelation, with various possible values for the power $p$. Note that $p$ is assumed known. An important difference in the implementation of the fixed-point algorithm (for approximating the root of the GE-EV estimating equation) is that the algorithm must be appropriately modified as a function of $p$. It is observed here that this implementation is quite fast, even for a data size as large as 8196.