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

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.

Keywords

• expectation values
• variance
• optimization
• fitting methods
• Lp Norms
• time series analysis