On the convergence and law of large numbers for the non-Euclidean Lp-means

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Abstract

This paper describes and proves two important theorems that compose the Law of Large Numbers for the non-Euclidean Lp-means, known to be true for the Euclidean L2-means: Let the Lp-mean estimator, which constitutes the specific functional that estimates the Lp-mean of N independent and identically distributed random variables; then, (i) the expectation value of the Lp-mean estimator equals the mean of the distributions of the random variables; and (ii) the limit N ∞ of the Lp-mean estimator also equals the mean of the distributions.

Original languageEnglish (US)
Article number217
JournalEntropy
Volume19
Issue number5
DOIs
StatePublished - May 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy

Keywords

  • Expectation values
  • Fitting methods
  • L norms
  • Optimization
  • Time series analysis
  • Variance

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