Algorithms 2011, 4(2), 115-130; doi:10.3390/a4020115
Article

Alternatives to the Least Squares Solution to Peelle’s Pertinent Puzzle

1 Statistical Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 2 Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 3 Nuclear and Particle Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 4 Decision Applications, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
* Author to whom correspondence should be addressed.
Received: 28 March 2011; in revised form: 1 June 2011 / Accepted: 8 June 2011 / Published: 23 June 2011
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Abstract: Peelle’s Pertinent Puzzle (PPP) was described in 1987 in the context of estimating fundamental parameters that arise in nuclear interaction experiments. In PPP, generalized least squares (GLS) parameter estimates fell outside the range of the data, which has raised concerns that GLS is somehow flawed and has led to suggested alternatives to GLS estimators. However, there have been no corresponding performance comparisons among methods, and one suggested approach involving simulated data realizations is statistically incomplete. Here we provide performance comparisons among estimators, introduce approximate Bayesian computation (ABC) using density estimation applied to simulated data realizations to produce an alternative to the incomplete approach, complete the incompletely specified approach, and show that estimation error in the assumed covariance matrix cannot always be ignored.
Keywords: approximate Bayesian computation using density estimation; mean squared error; Peelle’s puzzle

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MDPI and ACS Style

Burr, T.; Graves, T.; Hengartner, N.; Kawano, T.; Pan, F.; Talou, P. Alternatives to the Least Squares Solution to Peelle’s Pertinent Puzzle. Algorithms 2011, 4, 115-130.

AMA Style

Burr T, Graves T, Hengartner N, Kawano T, Pan F, Talou P. Alternatives to the Least Squares Solution to Peelle’s Pertinent Puzzle. Algorithms. 2011; 4(2):115-130.

Chicago/Turabian Style

Burr, Tom; Graves, Todd; Hengartner, Nicolas; Kawano, Toshihiko; Pan, Feng; Talou, Patrick. 2011. "Alternatives to the Least Squares Solution to Peelle’s Pertinent Puzzle." Algorithms 4, no. 2: 115-130.

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