Detection performance of some nonparametric rank tests and an application to radar

Importance Sampling Applied to Simulation of False Alarm Statistics

“…Let us generalize the situation by assuming arbitrary weights in the summation as K y =F(x 1,..,xK) = ,ak k=l (41) i where {Xk } is the set of independent exponential j random variables on input with a mean value I_.…”

“…The distribution function of y is given by K~~~~~~K K 35~~~~~~~~~~~~~~ In Fig. 6 we have used importance sampling to estimate Q(Y) for K = 2 and N = 1000.-The ratio < \~o f weights used in (41) varied from 0.48/0.52 (resulting in essentially a chi-square distribution with 4 degrees of freedom) to 0.05/0.95, with the sum of weights being unity in all cases. For each of the cases, the procedure was optimized in the 16 18 neighborhood of Q(Y)_ 10-6 (e.g., X-M= 10.7x-for the 0.25/0.7 5 case).…”

“…With this example we can create the following io-4~" '_'I_''_''_l'_'"_ll_I_'__'_________i_'______l_ll____l__l__l__l interesting situation: let K = 2 so that the weight used in importance sampling in (40) will be based on two input variables; however, let one of the weights ak in (41 ) be zero so that the output y will be exponentially distributed. From one replication 10 5 to the other we can even interchange the ak without affecting the distribution function of y.…”

Permutation tests for nonparametric detection

“…Interesting classical tutorial papers about nonparametric detection are due to Carlyle and Thomas [18] and Thomas [19]. Applications of rank tests to radar detection can be found in [20][21][22][23][24] and references therein. Other rank applications to (wireless) communications are, for example, in [25][26][27][28][29] and references therein.…”

“…Other rank applications to (wireless) communications are, for example, in [25][26][27][28][29] and references therein. Finally, although rank tests have been applied to detection [16][17][18][19][20][21][22][23][24][25][26][27][28][29], the more general family of permutation tests has seldom been applied to radar detection [30][31][32][33][34][35], at least, as far as the authors know. Now, some comments on the methodology of test optimization are required.…”