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Slides17-2010

# Slides17-2010 - Denition of Estimator and Choosing among...

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Definition of Estimator and Choosing among Estimators: Lecture XVII Charles B. Moss October 9, 2010 Charles B. Moss () Definition of Estimator October 9, 2010 1 / 19

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1 What is an Estimator? Properties of the Sample Mean 2 Estimators in General Nonparametric Estimation Properties of Estimators Measures of Closeness Charles B. Moss () Definition of Estimator October 9, 2010 2 / 19
What is an Estimator? In the next several lectures we will be discussing statistical estimators and estimation. 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. 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. This estimation is typically based on a sample of outcomes drawn from the population instead of the population itself. Charles B. Moss () Definition of Estimator October 9, 2010 3 / 19

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Common point estimators are the sample moments Sample Mean ¯ X = 1 n n i =1 X i (1) Sample Variance S 2 X = 1 n n i =1 ( X t ¯ X ) 2 = 1 n n i =1 X 2 t ( ¯ X ) 2 (2) The k th sample moment around zero M k = 1 n n i =1 X k i (3) Charles B. Moss () Definition of Estimator October 9, 2010 4 / 19
Continued The k th moment around the mean ˜ M k = 1 n n i =1 ( X i ¯ X ) k (4)

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Slides17-2010 - Denition of Estimator and Choosing among...

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