Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Quantlet: mve Description: Computes the minimum volume ellipsoid estimate of location

 Usage: z = mve(x{, cutoff}) Input: x n x p matrix (n observations of dimension p) cutoff an optional scalar defining the threshold for rejection of observations; by default, it equals 0.975 quantile of the chi-square distribution with n degrees of freedom Output: z.mve p x 1 vector containing the estimate of location z.mdist n x 1 vector containing Mahalanobis distances for all observations z.rdist n x 1 vector containing robust distances for all observations z.weights n x 1 vector containing 0 (for observations that have their robust distance greater then "cutoff", i.e., they are too far from the center of the data) or 1 (otherwise) z.matcov p x p robust covariance matrix z.matcor p x p robust correlation matrix

Example:
```library("robtech")
;
; simulate data
;
randomize(101)
x = #(uniform(98),10,100)
;
; estimate the location by mve
;
z = mve(x)
z.mve
; estimate the location by median and mean
;
median(x)
mean(x)

```
Result:
```Contents of mve
[1,]  0.48199

Contents of med
[1,]  0.49727

Contents of mean
[1,]   1.5723
```
Example:
```library("robtech")
;
; simulate data
;
randomize(1)
x = uniform(100,2)|(2*(uniform(20,2)-0.5))
;
; estimate the location by mve
;
z = mve(x)
z.mve
;
; draw a depth graph and median
;
d = createdisplay(1,1)
dat = x
col = z.weights
est = z.mve'
setmaskp(est,4,12,15)    ; mve is red big star
show(d, 1, 1, dat, est)
setgopt(d, 1, 1, "title", "Minimum volume ellipsoid")

```
Result:
```There are two types of output. First, in the output window, the
following estimate appears:
Contents of mve
[1,]  0.47337
[2,]  0.40312

Moreover, there is also a graph showing the minimum volume ellipsoid