A review of some adaptive statistical techniques

Abstract

We present several methods for full, partial, and practical adaptation. Selector statistics that are measures of skewness, peakedness, and tailweight are used, primarily in estimating loca-tion in some single-sample situations. We note several practical adaptive techniques in current use, including illustrations in-volving stepwise regression, analysis of variance, ridge regres-sion, and splines. We suggest some areas in which future develop-ment of adaptive methods is needed:density estimation; M, R, and L estimation in regression; and dependent data. There is also a need to develop better selector statistics.

Keywords:

• Adaptive methods
• robust M, R, and L estimation
• density estimation
• selector statistics
• general-ized cross validation
• ridge regression
• variable selection
• splines
• testing independence