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Entropy 2017, 19(5), 217; doi:10.3390/e19050217

On the Convergence and Law of Large Numbers for the Non-Euclidean Lp -Means

Space Science and Engineering, Southwest Research Institute, San Antonio, TX 78238, USA
Academic Editors: Antonio Maria Scarfone and Kevin Knuth
Received: 18 January 2017 / Revised: 13 April 2017 / Accepted: 9 May 2017 / Published: 11 May 2017
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Abstract

This paper describes and proves two important theorems that compose the Law of Large Numbers for the non-Euclidean L p -means, known to be true for the Euclidean L 2 -means: Let the L p -mean estimator, which constitutes the specific functional that estimates the L p -mean of N independent and identically distributed random variables; then, (i) the expectation value of the L p -mean estimator equals the mean of the distributions of the random variables; and (ii) the limit N of the L p -mean estimator also equals the mean of the distributions. View Full-Text
Keywords: expectation values; variance; optimization; fitting methods; Lp Norms; time series analysis expectation values; variance; optimization; fitting methods; Lp Norms; time series analysis
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Livadiotis, G. On the Convergence and Law of Large Numbers for the Non-Euclidean Lp -Means. Entropy 2017, 19, 217.

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