The Entropy Concentration Theorem (ECT; Edwin, 1982) states that if \(N\) is large enough, then \(100(1-F)\)% of all \(\bold{p*}\) and \(\Delta H\) is determined by the upper tail are \(1-F\) of a \(\chi^2\) distribution, with \(DF = q - m - 1\) (which equals \(8\) in a surrogate evaluation context).
Usage
ECT(Perc=.95, H_Max, N)
Value
An object of class ECT with components,
Lower_H
The lower bound of the requested interval.
Upper_H
The upper bound of the requested interval, which equals \(H_Max\).
Arguments
Perc
The desired interval. E.g., Perc=.05 will generate the lower and upper bounds for \(H(\bold{p})\) that contain \(95\%\) of the cases (as determined by the ECT).
H_Max
The maximum entropy value. In the binary-binary setting, this can be computed using the function MaxEntICABinBin.
N
The sample size.
Author
Wim Van der Elst, Paul Meyvisch, & Ariel Alonso
References
Alonso, A., Van der Elst, W., & Molenberghs, G. (2016). Surrogate markers validation: the continuous-binary setting from a causal inference perspective.