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Update documentation
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aadler committed Jun 20, 2024
1 parent 554a6d7 commit 68e66a4
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions man/robScale.Rd
Original file line number Diff line number Diff line change
Expand Up @@ -56,10 +56,10 @@ to\deqn{\frac{1}{n}\sum_{i = 1}^n\rho\left(\frac{x_i - T_n}{S_n}\right) = \beta
where \eqn{T_n}{Tn} is fixed at \code{median(x)} and \eqn{\beta} is fixed at
0.5. The \eqn{\rho}-function selected by Rousseeuw & Verboven is based on the
square of the \eqn{\psi}-function used in \code{\link{robLoc}}. Specifically
\deqn{\rho_{log}(x) = \psi_{log}^2\left(\frac{x}{0.3739}\right)}{\rho(x) =
\psi^2(x / 0.3739)}
The 0.3739 is needed for \eqn{\beta} to be 0.5.
}
\deqn{\rho_{log}(x) = \psi_{log}^2\left(\frac{x}{0.37394112142347236}\right)
}{\rho(x) = \psi^2(x / 0.37394112142347236)}
The constant 0.37394112142347236 is necessary so that
\deqn{\beta = \int\rho(u)\;d\Phi(u)=0.5}{\beta = Int\rho(u)d\Phi(u)=0.5}

\references{
Rousseeuw, Peter J. and Verboven, Sabine (2002) Robust estimation in very small
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