# estimateSd: Robust standard deviation estimator In jointseg: Joint Segmentation of Multivariate (Copy Number) Signals

## Description

Estimate standard deviation of an unimodal signal with possible changes in mean

## Usage

 1 estimateSd(y, method = c("Hall", "von Neumann")) 

## Arguments

 y A numeric vector method Method used to estimate standard deviation

## Details

von Neumann's estimator is proportional to the mean absolute deviation (mad) of the first-order differences of the original signals: mad(diff(y). By construction this estimator is robust to 1) changes in the mean of the signal (through the use of differences) and 2) outliers (through the use of mad instead of mean).

The proportionality constant 1/√ 2 \times 1/Φ^{-1}(3/4) ensures that the resulting estimator is consistent for the estimation of the standard deviation in the case of Gaussian signals.

Hall's estimator is a weigthed sum of squared elements of y. Let m=3. sigma^2 = (∑_{k=1}^{n-m}∑_{j=1}^{m+1}(\code{wei[i]}\code{y}[i+k])^2)/(n-m)

## Author(s)

Morgane Pierre-Jean and Pierre Neuvial

## References

Von Neumann, J., Kent, R. H., Bellinson, H. R., & Hart, B. T. (1941). The mean square successive difference. The Annals of Mathematical Statistics, 153-162.

Peter Hall, J. W. Kay and D. M. Titterington (1990). Asymptotically Optimal Difference-Based Estimation of Variance in Nonparametric Regression Biometrika,521-528

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 n <- 1e4 y <- rnorm(n) ## a signal with no change in mean estimateSd(y) estimateSd(y, method="von Neumann") sd(y) mad(y) z <- y + rep(c(0,2), each=n/2) ## a signal with *a single* change in mean estimateSd(z) estimateSd(z, method="von Neumann") sd(z) mad(z) z <- y + rep(c(0,2), each=100) ## a signal with many changes in mean estimateSd(z) estimateSd(z, method="von Neumann") sd(z) mad(z) 

jointseg documentation built on May 2, 2019, 6:10 a.m.