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. P...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 u if and only if the limit of logarithm expectation of x approaches logarithm of u. 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.展开更多
文摘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 u if and only if the limit of logarithm expectation of x approaches logarithm of u. 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.
