Motivated by the advantages of using multiple antennas cognitive radio for a SS purpose as discussed in the above two paragraphs, in this manuscript, by relying on a sample covariance matrix (SCM), we heuristically formulated a

test statistic (TS).

(1) The supremum is the maximum

test statistic over the range of possible break dates.

Specifically, we report partial [R.sup.2], F-statistics for excluded instruments, and Cragg-Donald Wald

test statistic for weak instruments.

Again, following MacKinlay (1997), the

test statistic for the sign test is calculated as

If the

test statistic is positive it means that the OS mean is higher than the TS mean.

For example, some of these tests require complete specification of the null distribution, some require computation of critical values to be done for each specified null distribution, and some require ordering of the sample data when computing the

test statistic. Generally, most of these tests are not supported when certain combinations of parameters of a specified distribution are estimated.

The

test statistic was derived using the maximum likelihood ratio test (MLRT) method.

In the case of Subject 1, recorded median tension drop was from 222.6 kPa to 110.3 kPa, and the

test statistic had p = 0.0022.

In this study, various goodness of fit criteria such as Sequential Modified Likelihood Ratio

Test Statistic (LR), Final Prediction Error (FPE), Akaike Information Criterion (AIC), Schwarz Information Criterion (SC) and Hannan-Quinn Information Criterion (HQ) were measured.

These two estimates are now comparable and can be used to form a

test statistic [I.sub.test,i] as

In addition to using various letters (F, t, U, and H, for example), each of the results for these statistical tests display a number in parentheses, which appears just after the designation of the

test statistic letter.

Explicitly, the Baklizi

test statistic can be written as follows: