# ER: Robust EM-algorithm ER In modi: Multivariate outlier detection and imputation for incomplete survey data

## Description

The `ER` function is an implementation of the ER-algorithm of Little and Smith (1987).

## Usage

 ```1 2``` ```ER(data, weights, alpha = 0.01, psi.par = c(2, 1.25), em.steps = 100, steps.output = FALSE, Estep.output=FALSE, tolerance=1e-6) ```

## Arguments

 `data` a data frame or matrix `weights` sampling weights `alpha` probability for the quantile of the cut-off `psi.par` further parameters passed to the psi-function `em.steps` number of iteration steps of the EM-algorithm `steps.output` if `TRUE` verbose output `Estep.output` if `TRUE` estimators are output at each iteration `tolerance` convergence criterion (relative change)

## Details

The M-step of the EM-algorithm uses a one-step M-estimator.

## Value

 `sample.size ` number of observations `number.of.variables ` Number of variables `significance.level` `alpha` `computation.time` Elapsed computation time `good.data` Indices of the data in the final good subset `outliers` Indices of the outliers `center` Final estimate of the center `scatter` Final estimate of the covariance matrix `dist` Final Mahalanobis distances `rob.weights` Robustness weights in the final EM step

Beat Hulliger

## References

Little, R. and P. Smith (1987). Editing and imputation for quantitative survey data. Journal of the American Statistical Association, 82, 58-68.

`BEM`
 ```1 2 3 4``` ```data(bushfirem) data(bushfire.weights) det.res<-ER(bushfirem, weights=bushfire.weights,alpha=0.05,steps.output=TRUE,em.steps=100,tol=2e-6) PlotMD(det.res\$dist,ncol(bushfirem)) ```