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The maximum eigenvalue test is based on Eq. (2).
The first test is the trace test and the second is the maximum eigenvalue test.
(Johansen 1988) derived two tests for cointegration: the λ − max (or maximum eigenvalue test) and the trace test.
In this paper, the trace statistic and maximum eigenvalue test are used to determine whether there is a co-integration relationship.
Additional file 2: Table S2 shows that there are five cointegration equations based on the trace test, and three cointegration equations based on the maximum eigenvalue test.
The Johansen co-integration test has two test statistics: the trace test statistic (mathop lambda nolimits_{text{trace}}) and the maximum eigenvalue test statistic (mathop lambda nolimits_{hbox{max} }), which are shown in Eq. (4) and Eq. (5).
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From the perspective of minimizing the "worst-direction" error represented by the maximum eigenvalue, PRBSs are not the best test signals in the case that disturbances are colored noises.
We use a rank one Gaussian perturbation to derive a smooth stochastic approximation of the maximum eigenvalue function.
The unknown maximum eigenvalue of actuator efficiency loss factors is estimated online.
Therefore it makes sense to measure the characteristic time to convergence τ using the mean lifetime of an exponential decay process which in turn can be approximated by the maximum eigenvalue of a corresponding matrix.
We then combine this smoothing result with an optimal smooth stochastic optimization algorithm to produce an efficient method for solving maximum eigenvalue minimization problems.
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