Algorithms 2011, 4(1), 28-39; doi:10.3390/a4010028
Article

Defense of the Least Squares Solution to Peelle’s Pertinent Puzzle

Tom Burr 1,* email, Toshihiko Kawano 2 email, Patrick Talou 2 email, Feng Pan 3 email and Nicolas Hengartner 4 email
1 Statistical Sciences, Los Alamos National Laboratory, Los Alamos NM, USA 2 Nuclear and Particle Physics, Los Alamos National Laboratory, Los Alamos NM, USA 3 Decision Applications, Los Alamos National Laboratory, Los Alamos NM, USA 4 Information Sciences, Los Alamos National Laboratory, Los Alamos NM, USA
* Author to whom correspondence should be addressed.
Received: 6 December 2010; in revised form: 15 January 2011 / Accepted: 7 February 2011 / Published: 15 February 2011
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Abstract: 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.
Keywords: Peelle’s puzzle; mean squared error; measurement error modeling

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Cite This Article

MDPI and ACS Style

Burr, T.; Kawano, T.; Talou, P.; Pan, F.; Hengartner, N. Defense of the Least Squares Solution to Peelle’s Pertinent Puzzle. Algorithms 2011, 4, 28-39.

AMA Style

Burr T, Kawano T, Talou P, Pan F, Hengartner N. Defense of the Least Squares Solution to Peelle’s Pertinent Puzzle. Algorithms. 2011; 4(1):28-39.

Chicago/Turabian Style

Burr, Tom; Kawano, Toshihiko; Talou, Patrick; Pan, Feng; Hengartner, Nicolas. 2011. "Defense of the Least Squares Solution to Peelle’s Pertinent Puzzle." Algorithms 4, no. 1: 28-39.

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