Compute Design Adaptive Scale estimate

This function calculates a Design Adaptive Scale estimate for a given MM-estimate. This is supposed to be a part of a chain of estimates like SMD or SMDM.

lmrob..D..fit(obj, x=obj$x, control = obj$control,
              mf,
              method = obj$control$method)

Arguments

obj

lmrob-object based on which the estimate is to be calculated.

x

the design matrix; if missing, the method tries to get it from obj$x and if this fails from obj$model.

control

list of control parameters, as returned by lmrob.control.

mf

defunct.

method

optional; the method used for obj computation.

Details

This function is used by lmrob.fit and typically not to be used on its own. Note that lmrob.fit() specifies control potentially differently than the default, but does use the default for method.

Value

The given lmrob-object with the following elements updated:

scale

The Design Adaptive Scale estimate

converged

TRUE if the scale calculation converged, FALSE other.

References

Koller, M. and Stahel, W.A. (2011), Sharpening Wald-type inference in robust regression for small samples, Computational Statistics & Data Analysis 55(8), 2504–2515.

See also

lmrob.fit, lmrob

Author

Manuel Koller

Examples

data(stackloss)
## Compute manual SMD-estimate:
## 1) MM-estimate
m1 <- lmrob(stack.loss ~ ., data = stackloss)
## 2) Add Design Adaptive Scale estimate
m2 <- lmrob..D..fit(m1)
print(c(m1$scale, m2$scale))
#> [1] 1.912355 2.650919

summary(m1)
#> 
#> Call:
#> lmrob(formula = stack.loss ~ ., data = stackloss)
#>  \--> method = "MM"
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -10.50974  -1.43819  -0.09134   1.02503   7.23113 
#> 
#> Coefficients:
#>              Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -41.52462    5.29780  -7.838 4.82e-07 ***
#> Air.Flow      0.93885    0.11743   7.995 3.68e-07 ***
#> Water.Temp    0.57955    0.26296   2.204   0.0416 *  
#> Acid.Conc.   -0.11292    0.06989  -1.616   0.1246    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Robust residual standard error: 1.912 
#> Multiple R-squared:  0.9593,	Adjusted R-squared:  0.9521 
#> Convergence in 17 IRWLS iterations
#> 
#> Robustness weights: 
#>  observation 21 is an outlier with |weight| = 0 ( < 0.0048); 
#>  2 weights are ~= 1. The remaining 18 ones are summarized as
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>  0.1215  0.8757  0.9428  0.8721  0.9797  0.9978 
#> Algorithmic parameters: 
#>        tuning.chi                bb        tuning.psi        refine.tol 
#>         1.548e+00         5.000e-01         4.685e+00         1.000e-07 
#>           rel.tol         scale.tol         solve.tol          zero.tol 
#>         1.000e-07         1.000e-10         1.000e-07         1.000e-10 
#>       eps.outlier             eps.x warn.limit.reject warn.limit.meanrw 
#>         4.762e-03         1.692e-10         5.000e-01         5.000e-01 
#>      nResample         max.it       best.r.s       k.fast.s          k.max 
#>            500             50              2              1            200 
#>    maxit.scale      trace.lev            mts     compute.rd fast.s.large.n 
#>            200              0           1000              0           2000 
#>                   psi           subsampling                   cov 
#>            "bisquare"         "nonsingular"         ".vcov.avar1" 
#> compute.outlier.stats 
#>                  "SM" 
#> seed : int(0) 
summary(m2) ## the covariance matrix estimate is also updated
#> 
#> Call:
#> lmrob(formula = stack.loss ~ ., data = stackloss, method = "SMD")
#>  \--> method = "MM"
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -10.50974  -1.43819  -0.09134   1.02503   7.23113 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -41.5246     9.3676  -4.433 0.000365 ***
#> Air.Flow      0.9388     0.1230   7.636 6.84e-07 ***
#> Water.Temp    0.5796     0.3348   1.731 0.101505    
#> Acid.Conc.   -0.1129     0.1231  -0.917 0.371736    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Robust residual standard error: 2.651 
#> Multiple R-squared:  0.9593,	Adjusted R-squared:  0.9521 
#> Convergence in 17 IRWLS iterations
#> 
#> Robustness weights: 
#>  observation 21 is an outlier with |weight| = 0 ( < 0.0048); 
#>  2 weights are ~= 1. The remaining 18 ones are summarized as
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>  0.1215  0.8757  0.9428  0.8721  0.9797  0.9978 
#> Algorithmic parameters: 
#>        tuning.chi                bb        tuning.psi        refine.tol 
#>         1.548e+00         5.000e-01         4.685e+00         1.000e-07 
#>           rel.tol         scale.tol         solve.tol          zero.tol 
#>         1.000e-07         1.000e-10         1.000e-07         1.000e-10 
#>       eps.outlier             eps.x warn.limit.reject warn.limit.meanrw 
#>         4.762e-03         1.692e-10         5.000e-01         5.000e-01 
#>      nResample         max.it       best.r.s       k.fast.s          k.max 
#>            500             50              2              1            200 
#>    maxit.scale      trace.lev            mts     compute.rd fast.s.large.n 
#>            200              0           1000              0           2000 
#>                   psi           subsampling                   cov 
#>            "bisquare"         "nonsingular"         ".vcov.avar1" 
#> compute.outlier.stats 
#>                  "SM" 
#> seed : int(0)