Premium and Protection of Several Procedures For Dealing With Outliers When Sample Sizes Are Moderate to Large

In a recent paper, Tiao and Guttman (1967) discussed the use of adjusted residuals to analyze the behaviour in moderate to large samples of the premium and protection of Anscombe's rule (herein designated as the A(k)-rule) when sampling is from the N(μ, σ) distribution, μ is to be estimated;and where k outlying observations are suspected of being spurious (k = 1 and 2). A discussion of two other rules, Semi-Winsorization (S (1)-rule) and Winsorization (W (1)-rule), is given in Guttman and Smith (1969, 1971). This paper investigates the behaviour, for moderate to large n, of the A (k)), S (k)) and W (k))- rules, k = 1 and 2. To do this, we define rules based on adjusted residuals, which we shall denote as the A k , S k and W k rules. Expressions for the premium and protection of the S k and W k rules are derived, and contrasted with these characteristics of the A k rule, obtained by Tiao and Guttman (1967). Some discussion of the case when σ2 is unknown is also included. Here we assume that there is an independent estimate of σ2, and we use rules with a different, type of adjusted residual.