NotesNov12 - Sampling statistics and estimators Recall: a...

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Unformatted text preview: Sampling statistics and estimators Recall: a sample is a collection of observa- tions X 1 = x 1 ,X 2 = x 2 ,...,X n = x n . Most of statistics is based on assuming that the observations forming a sample are iid random variables . Recall: a statistic is any function of the sam- ple, i.e. a function of X 1 ,...,X n . Examples of statistics : X n = X 1 + X 2 + ... + X n n , M n = max( X 1 ,...,X n ) . Since a statistic is a function of random obser- vations, it is itself a random variable. A statistic is typically used to estimate an unknown parameter of the distribution of the observations X 1 ,X 2 ,...,X n , a popula- tion parameter . Such statistic is called an estimator of the population parameter. Example : The sample mean X n is often used as an estimator of the (population) mean = EX i . Recall: an estimator d = d ( X 1 ,...,X n ) of a population parameter is called unbiased if E ( d ( X 1 ,...,X n )) = ....
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This note was uploaded on 12/03/2010 for the course OR&IE 3500 taught by Professor Samorodnitsky during the Fall '10 term at Cornell University (Engineering School).

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NotesNov12 - Sampling statistics and estimators Recall: a...

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