Lecture4 - SUNY at Albany - Department of Economics Eco 320...

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Unformatted text preview: SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference Statistical Inference SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference 1. Introduction A. Population vs. Sample Population : the totality of all possible outcomes of an issue of interest. Sample : a subset of a population SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference 1. Introduction A. Population vs. Sample Population : the totality of all possible outcomes of an issue of interest. Sample : a subset of a population B. Parameters vs. Statistics/Estimators A parameter is a fixed number that describes the population. The actual value of this number is unknown. A statistic is a random variable that describes a random sample. The value of a statistic (an estimate) is known when we have taken a sample, but it changes from sample to sample. Statistics estimate parameters. 1. Introduction A. The process of generalizing from the sample value (e.g. ,) to the population value (e.g., ) is the essence of statistical inference. SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference 2. Estimation A. We want to study some population of interest. Which distribution does the population follow? What are the actual value(s) of the population parameter(s)? SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference 2. Estimation A. We want to study some population of interest. Which distribution does the population follow? What are the actual value(s) of the population parameter(s)? B. Choose a random sample from the population and use sample statistics to estimate the truth about the whole population. SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference 2. Estimation (continued) C. Point Estimate A statistic, is a r.v. (e.g. ) Its value will vary from sample to sample. How reliable it is? D. Interval Estimate A interval that most likely to include true parameter (e.g. ). Key ideas: sampling/probability distribution of an estimator. (e.g. ~( , 2 ) ) 2. Estimation (continued) A. In Appendix C, we saw that = / ~ 0, 1 and = / if we do not know . SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference 2. Estimation (continued) A. Critical t value Upper critical t value and lower critical t value E.g for a sample of 28 observations 2.052 2.052 = 0.95 2.052 / 2.052 = 0.95 2.052 + 2.052 = 0.95(1) Provideaintervalestimatorofthetrue . SUNY at Albany - Department of Economics Eco 320 Economic Statistics Inference 2. Estimation (continued) 2....
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Lecture4 - SUNY at Albany - Department of Economics Eco 320...

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