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Article
Author(s)

Loc Nguyen

Affiliation(s)

Vietnam Institute of Mathematics, Vietnam

ABSTRACT

In statistical theory, a statistic that is function of sample observations is used to estimate distribution parameter. This statistic is called unbiased estimate if its expectation is equal to theoretical parameter. Proving whether or not a statistic is unbiased estimate is very important but this proof may require a lot of efforts when statistic is complicated function. Therefore, this research facilitates this proof by proposing a theorem which states that the expectation of variable x > 0 is μ if and only if the limit of logarithm expectation of x approaches logarithm of μ. In order to make clear of this theorem, the research gives an example of proving correlation coefficient as unbiased estimate by taking advantages of this theorem.

KEYWORDS

Logarithm expectation, correlation coefficient, unbiased estimate.

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References
[1] Sean Borman. The Expectation Maximization Algorithm - A short tutorial. Department of Electrical Engineering, University of Notre Dame, South Bend, Indiana. Last updated January 09, 2009.
[2] Douglas C. Montgomery, George C. Runger. Applied Statistics and Probability for Enginners, 3rd edition. Copyright 2003 © John Wiley & Son, Inc, 2003. ISBN: 0-471-20454-4.
[3] Jeff A. Bilmes. A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models. International Computer Science Institute, Berkeley CA, 94704 and Computer Science Division, Department of Electrical Engineering and Computer Science, U.C. Berkeley, TR-97-021, April 1998.  
[4] Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye. Probability & Statistics for Engineers & Scientists, 9th edition. Copyright © 2012, 2007, 2002 Pearson Education, Inc. ISBN: 978-0-321-62911-1. 

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