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Unformatted text preview: Chapter 7 Using Statistics for Inference and Estimation Statistical Inference • Inference is a process of figuring out something unknown based on something known. • Statistical Inference is estimating unknown population parameters from a sample Point Estimation • Estimation of the value of a parameter as a single point from the value of a statistic. • Sample mean ( ) is a point estimate of population ( μ ). X Basic Properties of “GOOD” Estimator • Unbiasness: An estimator is unbiased if its expectation value is equal to the true value disregarding the size of the sample. • Consistency: An estimator is consistent if it tends to the true value when the number of data points N tends to infinity. • Efficiency: An estimator is efficient if its variance is small. Unbiased Estimator • A statistic with mean value that equals the value of the parameter it estimates. • The sample mean ( ) from a sample of size N is an unbiased estimate of the population mean because if we take all possible random samples of N from the population, the mean of these samples is equal to the population mean. X Consistent Estimator • A statistic for which the probability that the value of the statistic is closer to the value of the parameter increases as the sample size increases. • As N increases, the statistic (e.g. sample mean) is a better estimate of the population parameter (e.g. population mean). Statistical Inference • Estimating unknown population parameters from known...
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This note was uploaded on 11/30/2009 for the course HP 400m at USC.
 '07
 Nezami,Borovay

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