Contrasting Alternatives to Least Squares in Regression Using Diagnostics for Identifying Influential Data.

Area of Science:

• Statistics
• Econometrics
• Data Analysis

Background:

• Regression analysis is fundamental in statistical modeling.
• Estimating regression coefficients accurately is crucial for reliable inference.
• Various alternative methods exist, each with underlying assumptions.

Purpose of the Study:

• To identify implicit assumptions of alternative regression coefficient estimators.
• To compare these assumptions using diagnostic measures.
• To determine optimal use cases for each estimator based on its assumptions.

Main Methods:

• Utilized regression diagnostic measures: leverage and influence.
• Formulated these measures for Ridge, Stein, principal component, and equal weight estimators.
• Contrasted the competing assumptions inherent in each method.

Main Results:

• Implicit assumptions for Ridge, Stein, principal component, and equal weight estimators were identified.
• Leverage and influence measures were formulated for these estimators.
• Situations favoring each alternative estimator were delineated based on implicit priors.

Conclusions:

• Understanding implicit assumptions is key to selecting appropriate regression estimators.
• Diagnostic measures provide a framework for comparing estimator assumptions.
• The choice of estimator should be guided by the specific data characteristics and prior beliefs.