Estimate of the efficiency of informative Fischer's criteria in the space of informative signs under restricted resources (Q2743060)

One of the methods for estimating the efficiency of informative Fischer's type criteria in the space of informative signs with restricted resources is offered. Let \(\Lambda^l= \{\lambda\in R^n\mid \lambda_i\in\{0,1\}\), \(\sum_{i= 1}^n\lambda_i=l\}\) and \(\Lambda^l(c)= \{\lambda\in \Lambda^l\mid(\lambda,c) \leq c_0\}\), where \(l\leq n\), \(c\in R^n\). It is proved (Theorem 1) that the function NEWLINE\[NEWLINE F(l)= \max_{\lambda\in\Lambda^l(c)}\frac{(a,\lambda)}{(b,\lambda)},NEWLINE\]NEWLINE where \(a,b\in R^n\) has the property \(F(l)\leq F(l-1)\) for \(l\geq 2\).