MESTIMATORS Subcommand (EXAMINE command)

M-estimators are robust maximum-likelihood estimators of location. Four M-estimators are available for display in the M-Estimators table. They differ in the weights they apply to the cases. MESTIMATORS with no keywords produces Huber’s M-estimator with c=1.339; Andrews’ wave with c=1.34π; Hampel’s M-estimator with a=1.7, b=3.4, and c=8.5; and Tukey’s biweight with c=4.685.

HUBER(c). Huber’s M-estimator. The value of weighting constant c can be specified in parentheses following the keyword. The default is c=1.339.

ANDREW(c). Andrews’ wave estimator. The value of weighting constant c can be specified in parentheses following the keyword. Constants are multiplied by π. The default is 1.34π.

HAMPEL(a,b,c). Hampel’s M-estimator. The values of weighting constants a, b, and c can be specified in order in parentheses following the keyword. The default values are a=1.7, b=3.4, and c=8.5.

TUKEY(c). Tukey’s biweight estimator. The value of weighting constant c can be specified in parentheses following the keyword. The default is c=4.685.

ALL. All four above M-estimators. This is the default when MESTIMATORS is specified with no keyword. The default values for weighting constants are used.

NONE. No M-estimators. This is the default if MESTIMATORS is omitted.

Example

EXAMINE VARIABLE=CASTTEST /MESTIMATORS.
  • MESTIMATORS generates all four M-estimators computed with the default constants.

Example

EXAMINE VARIABLE=CASTTEST /MESTIMATORS=HAMPELS(2,4,8).
  • MESTIMATOR produces Hampel’s M-estimator with weighting constants a=2, b=4, and c=8.