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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)¡ Provide¡a¡interval¡estimator¡of¡the¡true¡ .¡ SUNY at Albany  Department of Economics Eco 320 Economic Statistics • Inference 2. Estimation (continued) 2....
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This note was uploaded on 02/08/2012 for the course ECON 320 taught by Professor Chan during the Spring '11 term at SUNY Albany.
 Spring '11
 Chan
 Economics

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