In the multivariate case, the problem of optimal or near optimal interpolation is much more difficult.
In the multivariate case, the delay margin can be bounded by constraint on the upper principal gains on sensitivity and complementary sensitivity of the closed-loop.
Generalizing the methods in Kalke and Richter (2013), Section 6 presents corresponding direct and acceptance-rejection methods and indicates how to extend to the dependent p-generalized multivariate case the classical and the rejecting polar methods in Box and Muller (1958) and Marsaglia and Bray (1964), respectively.
In the multivariate case the dynamically forecasted values are generated using all of the additional explanatory variables, but within the AR component of the model the lagged values of the dependent variable (tourism) are replaced by the predicted values once we cross the time of the critical event or intervention.
In the bivariate case, the KWII is always nonnegative, but in the multivariate case, the KWII can be positive or negative.
Since SVAR deals with the multivariate case, the definition of Granger causality becomes complex, because of the existence of multi-steps connectivities.
At very high (95%) confidence, no signals are detected for RX1D, while for the RX5D and multivariate cases only the anthropogenic (ANT) signal is detected, though the fingerprints are in general found to be noisy.
In statistics, various methods for selecting the bandwidth have been established for multivariate cases, including the minimum-risk procedure based on the integrated mean square error and the cross-validation method [refer to Silverman (1986) and Wand and Jones (1986) for reviews].
There are several GOF tests particularly proposed for the multivariate case, e.g., the nearest neighbor test which exploits the nearest neighbors [41], Mardia test which exploits the skewness and kurtosis [42] and Freidman Rafsky test which exploits the minimum spanning tree [43].
(1999), it is also possible to generalize the local regression procedure employed in the NN non-parametric regression to the multivariate case using the information contained in several time series.
