Stat_Chap7 - Parameter Estimation Chapter 7 (7-4.1,7-4.3...

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Parameter Estimation Chapter 7 (7-4.1,7-4.3 excluded)
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Inferential statistics Using sample data to draw conclusions about a population • Inferential statistics Parameter estimation (mean, variance, proportion) Confidence interval Testing hypotheses (statements about population) Linear regression
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Parameter estimation Interested in key parameters of the population: mean, variance etc. Draw a random sample, construct appropriate estimators How to measure accuracy and precision
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Precision and accuracy Accurate Precise Precise Not accurate Accurate Not precise Neither
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Top paying career Highest paid professionals in America Anesthesiologists X : salary; distribution of X unknown; interested in mean salary μ =E[X] Consider a random sample of size n : X 1 ,…, X n
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Random sampling A random sample X 1 , … , X n X 1 , … , X n are independent to not introduce bias Each X i is a representative of the population: has the same distribution as X i.i.d. (independent and identically distributed) Statistic : a function of the observations in a random sample. E.g., sample mean n X X X n / ) ... ( 1 + + =
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Point estimator Estimate the population mean μ Point estimator : estimate a parameter of the population θ by a function of the random sample Estimate the population variance σ 2 n X X X n / ) ... ( 1 + + = Θ ˆ = = n i i X X n S 1 2 2 ) ( 1 1
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Point estimate A point estimate of θ is a single numerical value of Suppose X 1 ,…,X 5 return x 1 =289,000, x 2 =331,000, x 3 =318,000, x 4 =276,000, x 5 =355,000 • Point estimate of the mean salary 800 , 313 $ 5 / ) ... ( 5 1 = + + = x x x Θ ˆ
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Sampling distribution What can be said about a point estimate / estimator Accuracy, precision Why one estimator is better than another?
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This note was uploaded on 05/04/2010 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

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Stat_Chap7 - Parameter Estimation Chapter 7 (7-4.1,7-4.3...

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