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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 ( ). 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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 '07
 Nezami,Borovay

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