A note on determining the number of outliers in a normal sample with unequal variances by least squares procedure

An outlier problem given by Clarke and Lewis [J. Appl. Stat. 25 (1998) 751] provides motivation to develop a least squares procedure for outliers when observations are distributed with the same mean but different variances. The criterion of the proposed procedure is to minimize the error sum of squares. One advantage of the procedure is easy and simple to compute than test procedure R suggested by Clarke and Lewis [J. Appl. Stat. 25 (1998) 751], since they need to use the complicated null distribution of R. Furthermore, the method is free from the effects of masking and swamping, when testing upper or lower outliers in normal samples. Results from simulation studies assessing the performance of the our proposed method are better than Clarke and Lewis [J. Appl. Stat. 25 (1998) 751]. Finally, we also use the proposed procedure to analyse the ore grade data (see Table 1 of Clarke and Lewis [J. Appl. Stat. 25 (1998) 751]).