From 4f3580837dfff6c708dd0db66f78d768c36b68bc Mon Sep 17 00:00:00 2001 From: Michael Mayer Date: Mon, 10 Jul 2023 23:37:15 +0200 Subject: [PATCH] Update README.md --- README.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/README.md b/README.md index f9847d56..38199415 100644 --- a/README.md +++ b/README.md @@ -315,34 +315,34 @@ $$ with $$ - B_{jkl} = \hat F_{jk}(x_j, x_k) + \hat F_{jl}(x_j, x_l) + \hat F_{kl}(x_k, x_l) + B_{jkl} = F_{jk}(x_j, x_k) + F_{jl}(x_j, x_l) + F_{kl}(x_k, x_l) $$ and $$ - C_{jkl} = \hat F_j(x_j) + \hat F_k(x_k) + \hat F_l(x_l). + C_{jkl} = F_j(x_j) + F_k(x_k) + F_l(x_l). $$ The squared and scaled difference between the two sides of the equation leads to the statistic $$ - H_{jkl}^2 = \frac{\frac{1}{n} \sum_{i = 1}^n \big[\hat F_{jkl}(x_{ij}, x_{ik}, x_{il}) - B^{(i)}_{jkl} + C^{(i)}_{jkl}\big]^2}{\frac{1}{n} \sum_{i = 1}^n \hat F_{jkl}(x_{ij}, x_{ik}, x_{il})^2}, + H_{jkl}^2 = \frac{\frac{1}{n} \sum_{i = 1}^n \big[\hat F_{jkl}(x_{ij}, x_{ik}, x_{il}) - B^i_{jkl} + C^i_{jkl}\big]^2}{\frac{1}{n} \sum_{i = 1}^n \hat F_{jkl}(x_{ij}, x_{ik}, x_{il})^2}, $$ where $$ - B^{(i)}_{jkl} = F_{jk}(x_{ij}, x_{ik}) + F_{jl}(x_{ij}, x_{il}) + F_{kl}(x_{ik}, x_{il}) + B^i_{jkl} = \hat F_{jk}(x_{ij}, x_{ik}) + \hat F_{jl}(x_{ij}, x_{il}) + \hat F_{kl}(x_{ik}, x_{il}) $$ and $$ - C^{(i)}_{jkl} = F_j(x_{ij}) + F_k(x_{ik}) + F_l(x_{il}). + C^i_{jkl} = \hat F_j(x_{ij}) + \hat F_k(x_{ik}) + \hat F_l(x_{il}). $$ -Similar remarks as for $H_{jk}$ apply. +Similar remarks as for $H^2_{jk}$ apply. #### Total interaction strength of all variables together