ch3-1 - Chapter 3 Review of Statistics (Part 1) Review of...

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Chapter 3 Review of Statistics (Part 1)
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Review of Statistics Suppose we want to know the mean of the distribution of earnings of recent college graduates. I One way is to perform an exhaustive survey of the population of workers. I However, such a comprehensive survey would be extremely expensive (U.S. Census cost $10 billion). I Instead, we can select 1,000 members of the population at random (random sampling). Using statistical methods, we can learn about characteristics of the population.
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Estimators Suppose you want to know the mean value of Y in a population, μ Y . I A natural way to estimate this mean is to compute Y from randomly sampled Y 1 , ..., Y n . I Another way is simply use the Y 1 . I Both Y and Y 1 is a function of the data, both are estimators of μ Y (there are many estimators). An estimator is a function of a sample of data to be drawn randomly from a population. I An estimator is a random variable. It has sampling distribution. An estimate is the numerical value of the estimator when it is actually computed using data from a specific sample. I An estimate is a nonrandom number.
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Desirable Characteristics of an Estimator There are many possible estimators, but what are desirable characteristics? Let b μ Y denote some estimator of μ Y . I b μ Y is an unbiased estimator of μ Y , if E ( b μ Y ) = μ Y , otherwise is b μ Y is biased . I b μ Y is a consistent estimator of μ Y , if b μ Y p μ Y . Let ˜ μ Y be another estimator of μ Y , and suppose that both b μ Y and ˜ μ Y are unbiased. I Then b μ Y is said to be more efficient than ˜ μ Y if var ( b μ Y ) < var ( ˜ μ Y ) .
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Properties of the Sample Average ¯ Y As shown in Ch.2: I E ( Y ) = μ Y , Y is an unbiased estimator of μ Y . I
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This note was uploaded on 11/20/2011 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Fall '10 term at Rutgers.

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ch3-1 - Chapter 3 Review of Statistics (Part 1) Review of...

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