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# ioe265f11-Lec15 - Lec15 Point Estimation Concepts IOE 265...

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Unformatted text preview: Lec15- Point Estimation Concepts IOE 265 - Fall 2011 1 1 Point Estimation Concepts and Methods 2 Topics I. Concepts of Point Estimation Biased Vs. Unbiased Estimators Minimum Variance Estimators Standard Error of a Point Estimate II. Point Estimation Methods A. Method of Moments (MOM) B. Methods of Maximum Likelihood (MLE) Lec15- Point Estimation Concepts IOE 265 - Fall 2011 2 3 I. Point Estimates Objective – obtain an estimate of a population parameter from a sample (e.g. sample mean, X-bar, is a point estimate of the population mean x ) Applications: Parameter Estimation Hypothesis Testing (and other inferential statistics methods) 4 Parameter Estimation Example Suppose you wish to estimate the population mean, ,. Some possible estimators include: Sample Mean, Sample Median, Sample Trimmed Mean Assume a sample from a population with true mean of 1000 is taken. which of the following sample statistics is the best estimator of the population mean? Sample Mean = 965.0 Sample Median = 1009.5 Sample Trim Mean = 971.4 Lec15- Point Estimation Concepts IOE 265 - Fall 2011 3 5 Parameter Estimates - Fit In practice, estimators (often referred to as -hat) have some level of error. Why? Because -hat is a function of the observed Xi’s (random variables) So, Where θ is the population parameter we wish to estimate (e.g. X-bar= -hat = x + estimation error) Thus, we may identify the “best estimator” as the one with: Least bias (unbiased) Minimum variance of estimation error (increase the likelihood that the observed parameter estimate represents the true parameter) error estimation ˆ 6 Biased Vs. Unbiased Estimator Bias - difference between the expected value of the statistic -hat and the parameter Unbiased Estimator: Example: X-bar is an unbiased estimated of (Bias = 0) Suppose X 1 , X 2 , .. X n are iid rv’s, with E(X i ) = ) ˆ ( E Bias n n n Xi E E X E n i .. 1 ) ( ) ˆ ( ) ( Lec15- Point Estimation Concepts...
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ioe265f11-Lec15 - Lec15 Point Estimation Concepts IOE 265...

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