Lecture 17-2007 - Definition of an Estimator and Choosing...

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Definition of an Estimator and Choosing  among Estimators Lecture XVII
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What is An Estimator? The book divides this discussion into the estimation of a single number such as a mean or standard deviation or the estimation of a range such as a confidence interval. At the most basic level, the definition of an estimator involves the distinction between a sample and a population. In general we assume that we have a random variable, X , with some distribution function.
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Next, we assume that we want to estimate something about that population, for example we may be interested in estimating the mean of the population or probability that the outcome will lie between two numbers. For example, in a farm-planning model we may be interested in estimating the expected return for a particular crop. In a regression context, we may be interested in estimating the average effect of price or income on the quantity of goods consumed.
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This estimation is typically based on a sample of outcomes drawn from the population instead of the population itself.
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Moment Estimators = = n i i X n X 1 1 ( 29 ( 29 2 1 2 1 2 2 1 1 X X n X X n S n i i n i i X - = - = = = = n i k i X n 1 1
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( 29 = - n i k i X X n 1 1 ( 29 ( 29 ( 29 = - - = = n i i i xy Y Y X X n S Y X Cov 1 1 , y x xy xy S S S = ρ
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Focusing on the sample versus population dichotomy for a moment, the sample image of X , denoted X * and the empirical distribution function for
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This note was uploaded on 07/18/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

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Lecture 17-2007 - Definition of an Estimator and Choosing...

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