for rank-based trimming. In practice, the choice of α can be based on the proportion of outliers observed in a boxplot or histogram of the D 2 $_{i}$s. The estimator ˆ Θ defined above belongs to the general class of M-estimators, w hich have well-known asymptotic properties (Van der Vaart, 1998, ch. 5). As shown in the Appendix, √$_{n}$ { vec( ˆ Θ ) − vec( Θ$_{0}$ ) } follows an approximate N( 0 , A − $^{1}$BA − $^{1}$) distribution for large n , with The matrices A and B can be easily estimated, replacing expectations by averages. This asymptotic distribution can be used, for instance, to test significance of the regression: if Θ$_{0}$ = O , Wald’s statistic Q = n vec( ˆ Θ ) T ˆ A ˆ B − $^{1}$ˆ A vec( ˆ Θ ) follows an approximate χ 2 pq distribution for large n , so we decide the regression is significant if Q ≥ χ 2 pq, 1 − α for a given level α . We can also construct marginal tests and confidence interva ls for the individual coefficients θ$_{kl}$ . In Section 3 we will study the accuracy of this asymptotic approximation. It is our experience that the distribution of ˆ Θ approaches normality quite fast, but the above “sand- wich formula” tends to underestimate the variance when the s ample size n is small. In that case it is better to use bootstrap estimators of the covariance matrix of vec( ˆ Θ ) . In this section we study by simulation the finite-sample beha vior of the estimators (10). To this end, we generated data from model (8) with U ∼ N( 0 , Λ ) and W ∼ N( 0 , Σ ) , where 8 3 Simulations A = 2E { ρ $^{′′}$( e ) w $^{2}$( U ) Σ − 1 0 RR T ⊗ UU $^{T}$} + I$_{q}$ ⊗ E { ρ $^{′}$( e ) w ( U ) UU $^{T}$} , (15) T B = E [ ρ $^{′}$( e ) } $^{2}$w$^{2}$( U ) RR ⊗ UU $^{T}$] . (16)