On the diversity of estimates

• Published in: Computational statistics & data analysis Vol. 34; no. 1; pp. 67 - 89
• Main Author: VISEK, J. A
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 28.07.2000; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Diagnostics by high breakdown point; Diversity of estimates; Exact sciences and technology; Heuristics of high breakdown point; Linear inference, regression; LMS and LTS — new algorithms; Mathematics; Probability and statistics; Sciences and techniques of general use; Selection of estimate; Statistics; Selection of estimate; Diagnostics by high breakdown point; LMS and LTS — new algorithms; Heuristics of high breakdown point; Diversity of estimates; Least median squares estimation; Least trimmed squares estimation; Diversity; Estimator diversity; Regression analysis; Diagnosis; Algorithm; Breakdown point
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/S0167-9473(99)00068-7

The presented examples of regression analysis of some real data sets below confirm that it is possible that various estimators may produce considerably different estimates. Such situation will be called diversity of estimates. Employing high breakdown point estimators, namely the least median of squares (LMS) and the least trimmed squares (LTS), the diversity of estimates is demonstrated. Two examples with the artificial data and a formal reflection of the diversity of estimates hint why the diversity of estimates takes place. The theoretical reflection also shows that the diversity of estimates may appear for any sample size. A proposal an how to select from the diverse estimates of model is given and illustrated in examples of real data sets.