Chapter 9 - Chapter 9. One- and Two-Sample Estimation...

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Unformatted text preview: Chapter 9. One- and Two-Sample Estimation Problems 9.1 Statistical Inference using sample data, we search the right value of unknown parameter. parameter : constants which determine the distribution. estimation : estimator hypothesis testing : reject H or not Population Sample Parameters Parameters 2 , Statistics Statistics 2 , x s Statistical procedure Inference Sampling technique Population Sample Parameters Parameters 2 , Statistics Statistics 2 , x s Statistical procedure Inference Sampling technique 9.2 Classical Methods of Estimation Point estimation Interval estimation Estimator : a random variable, a procedure to estimating a parameter using sample statistics Estimate : estimated value of a parameter, not a random variable parameter : , estimator : Unbiasedness : A statistic is said to be an unbiased estimator of the parameter if ( ) E = = Mean Squared Error (MSE) : If we consider all possible unbiased estimators of some parameter , the one with the smallest variance is called the most efficient estimator of 2 2 [ ] [( ) ] [ ] [ ( ) ] MSE E Var E = = + If is an unbiased estimator of [ ] [ ] MSE Var = Interval Estimation : interval [ , ] L U is (1 )100% confidence interval for [ ] 1 L U P < < = 9.3 Single Sample : Estimating the Mean 9....
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This note was uploaded on 10/02/2011 for the course STAT 3011 taught by Professor Wang,zhan during the Spring '09 term at Minnesota.

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Chapter 9 - Chapter 9. One- and Two-Sample Estimation...

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