ENMA 420-520 Lecture 6 Slides_1

# ENMA 420-520 Lecture 6 Slides_1 - Statistical Concepts for...

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Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #6 Estimation Using Confidence Intervals 11

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10/17/09 Point Estimators A point estimator is a rule or formula that specifies how to calculate a numerical estimate based on measurements contained in a sample. The single number that results from the calculation is called a point estimate. Note the “^” accent used for estimates; e.g. an estimate of is 22
10/17/09 Biased vs. Unbiased A point estimator is calculated from a sample and therefore possesses a sampling distribution. The bias b(θ) of a point estimator is: A point estimator is said to be unbiased if the expected value of the parameter estimate is equal to the 33

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10/17/09 Minimum Variance Unbiased Estimator A small variance of the sampling distribution means most of the parameter estimates will tend to be close to the parameter Therefore, two desired characteristics for designing estimates are Minimum Variance Unbiased 44
10/17/09 Finding Point Estimators Method of Moments Method of Maximum Likelihood Method of Least Squares Other Methods 55

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10/17/09 Method of Moments Kth population moment: E(Yk) Kth sample moment: So … for 1st sample moment: Population moment is the population mean Sample moment is the sample mean 66
10/17/09 Maximum Likelihood The likelihood function L of a sample of n observations y1, y2, …, yn is the joint probability function p(y1, y2, …, yn) when Y1, Y2, … , Yn are discrete random variables. The likelihood function L of a sample of n observations y1, y2, …, yn is the joint probability function f(y1, y2, …, 77

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10/17/09 Maximum Likelihood (Cont’d) For random samples of n observations on a random variable Y, the likelihood function is: L = p(y1)p(y2)…p(yn) for discrete and L = f(y1)f(y2)…f(yn) for continuous Let L be the likelihood of a sample 88
10/17/09

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ENMA 420-520 Lecture 6 Slides_1 - Statistical Concepts for...

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