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Defense of the least squares solution to Peelle’s pertinent puzzle. (English) Zbl 07042096
Summary: Generalized least squares (GLS) for model parameter estimation has a long and successful history dating to its development by Gauss in 1795. Alternatives can outperform GLS in some settings, and alternatives to GLS are sometimes sought when GLS exhibits curious behavior, such as in Peelle’s Pertinent Puzzle (PPP). PPP was described in 1987 in the context of estimating fundamental parameters that arise in nuclear interaction experiments. In PPP, GLS estimates fell outside the range of the data, eliciting concerns that GLS was somehow flawed. These concerns have led to suggested alternatives to GLS estimators. This paper defends GLS in the PPP context, investigates when PPP can occur, illustrates when PPP can be beneficial for parameter estimation, reviews optimality properties of GLS estimators, and gives an example in which PPP does occur.

62 Statistics
91 Game theory, economics, finance, and other social and behavioral sciences
Full Text: DOI
[1] Peelle, R.; ; Peelle’s Pertinent Puzzle: Washington DC, USA 1987; .
[2] Nichols, A.L.; ; International Evaluation of Neutron Cross Section Standards: Vienna, Austria 2007; .
[3] Chiba, S.; Smith, D.; ; A Suggested Procedure for Resolving an Anomaly in Least-Squares Data Analysis Known as Peelle’s Pertinent Puzzle and the General Implications for Nuclear Data Evaluation: Argonne, IL, USA 1991; .
[4] Zhao, Z.; Perey, R.; ; The Covariance Matrix of Derived Quantities and Their Combination: Oak Ridge, TN, USA 1992; .
[5] Hanson, K.; Kawano, T.; Talou, P.; Probabilistic Interpretation of Peelle’s Pertinent Puzzle; Melville, NY, USA 2005; .
[6] Burr, T.; Kawano, T.; Talou, P.; Hengartner, N.; Pan, P.; Alternatives to the Least Squares Solution to Peelle’s Pertinent Puzzle; 2010; . · Zbl 07042101
[7] Christensen, R.; ; Plane Answers to Complex Questions, The Theory of Linear Models: New York 1999; ,23-25.
[8] Burr, T.; Frey, H.; Biased Regression: The Case for Cautious Application; Techometrics: 2005; Volume 47 ,284-296.
[9] Sivia, D.; Data Analysis—A Dialogue With The Data; Advanced Mathematical and Computational Tools in Metrology VII: Lisbon, Portugal 2006; ,108-118.
[10] Jones, C.; Finn, J.; Hengartner, N.; Regression with Strongly Correlated Data; J. Multivariate Anal.: 2008; Volume 99 ,2136-2153. · Zbl 1149.62057
[11] Finn, J.; Jones, C.; Hengartner, N.; Strong Nonlinear Correlations, Conditional Entropy, and Perfect Estimation; Bayesian Inference and Maximum Entropy Methods in Science and Engineering: Melville, NY, USA 2007; ,954.
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