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The Slope of a Straight Line: A Phony Estimator
October 1996 (vol. 18 no. 10)
pp. 1051

Abstract—This note discusses an estimator for the slope of a straight line as proposed by Werman and Geyzel [1]. By computing its frequency distribution, it is demonstrated that the estimator is a fake; it possesses neither a first nor a second moment. Application leads therefore to completely erratic outcomes.

[1] M. Werman and Z. Geyzel, "Fitting a Second Degree Curve in the Presence of Error," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, pp. 207-211, 1995.
[2] M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, vol. 1, fifth ed. London: Griffin, 1958, chapter 11, p. 268.
[3] A. Popoulis, Probability, Random Variables, and Stochastic Processes, third ed. New York: McGraw-Hill, 1985, chapter 6-2, p. 137.
[4] M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, vol. 2, third ed. London: Griffin, 1961, chapter 28, p. 377.
[5] S. Wolfram, Mathematica, second ed. Reading, Mass.: Addison-Wesley, 1991.
[6] N.J.D. Nagelkerke and J. Strackee, "Fitting the Hill Equation to Data: A Statistical Approach," IEEE Trans. Biomed. Eng., vol. 29, pp. 467-469, June 1982.

Citation:
Jan Strackee, "The Slope of a Straight Line: A Phony Estimator," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 10, pp. 1051, Oct. 1996, doi:10.1109/34.541416
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