Small sample corrections for LTS and MCD

Abstract

Abstract. The least trimmed squares estimator and the minimum covariance determinant estimator [6] are frequently used robust estimators of regression and of location and scatter. Consistency factors can be computed for both methods to make the estimators consistent at the normal model. However, for small data sets these factors do not make the estimator unbiased. Based on simulation studies we therefore construct formulas which allow us to compute small sample correction factors for all sample sizes and dimensions without having to carry out any new simulations. We give some examples to illustrate the e¤ect of the correction factor.

Robust Bayesian regression with the forward search: theory and data analysis

“…Further correction is needed in finite samples. Pison et al (2002) use simulation to make such corrections in robust regression, but not for FS. The second effect is again connected with the value of c(m, n), which is small for small m/n (for example 0.00525 for 10%).…”

“…Many other robust methods, such as MM-and S-estimation (Maronna et al 2006), downweight observations in a more smooth way, resulting in weights that have values in [0,1]. As an example, we use the trimmed likelihood weights from the R package wle (Agostinelli 2001).…”

“…The foundations of robust statistical methods are presented in the books of Hampel et al (1986), of Maronna et al (2006) and of Huber and Ronchetti (2009). Book length treatments of robust regression include Rousseeuw and Leroy (1987) and Atkinson and Riani (2000).…”

The multivariate coefficient of variation for comparing serum protein electrophoresis techniques in external quality assessment schemes

“…The initial location estimate is then the average of these h points and the initial scatter estimate is their covariance matrix. Afterwards, the initial covariance matrix is multiplied by a consistency factor to obtain multivariate normality and a correction factor to be unbiased for small sample sizes [17]. The final covariance matrix y S is obtained by using a weighting step to achieve better efficiency (see -covMcd‖ function in the -robustbase‖ package of R 2.9.2 [18]).…”

“…However, this computer intensive method is sensitive to the presence of outlying observations. Therefore, outliers were first removed from the dataset based on the approach recommended in [17] and then the bootstrap was applied to each cleaned dataset. The robust multivariate CV was calculated for each electrophoretic technique using Eq.…”