TA5 - ECO2121: Methods of Economic Statistics TA5 18...

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ECO2121: Methods of Economic Statistics TA5 18 February 2009 We continue from TA4 the Exponential distribution. 1. Statistical Inference 統計推論 Two essential elements: Estimation and Hypothesis Testing . 2. Parametric Distribution Some types of distribution are characterized by some parameters, for instance, for Normal( μ , σ 2 ), μ and σ 2 are the parameters. Usually for frequentists , these parameters are unknown but fixed , so they have to be estimated by some sample statistics. 3. Estimation In the earliest stage, we say the sample mean and the sample variance S 2 are used to estimated the (population) mean E X = μ and the (population) variance Var[ X ] = σ 2 . In effect, there are different ways to estimate them, such as the median for μ . We call ± = ² ³ ´ µ ·¸¹ an estimator (a way to estimate), and the realization of it, º = » ¼ ½ ¾ ¿ ÀÁ an estimate (a realized/numerical value). Example: Consider
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TA5 - ECO2121: Methods of Economic Statistics TA5 18...

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