lect4_2010

# lect4_2010 - 1 27 Introduction to Econometrics Econ 322...

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Unformatted text preview: 1 / 27 Introduction to Econometrics Econ 322 Fall, 2010 Lecture 4: Review of Statistics I September 15, 2010 Lecture Plan Sampling Theory Estimation 2 / 27 1. The sampling distribution of the sample average 2. large sample approximations 3. Estimation 4. Properties of Estimators Sampling Theory triangleright Sampling Theory Random Sampling and the Sample Mean Sampling Distribution Properties of the Sample Average Large Sample Properties Estimation 3 / 27 Random Sampling and the Sample Mean Sampling Theory triangleright Random Sampling and the Sample Mean Sampling Distribution Properties of the Sample Average Large Sample Properties Estimation 4 / 27 square We typically do not get to observe the whole population of a random variable. Therefore we have to make do with a sample from the population. square Suppose that we randomly choose N draws from the population. Let this sample be denoted { X 1 , . . . , X N } This is called a random sample from the population. square Because the sampling is done on a random basis, X i , the i th draw from the population is a random variable. square Also, because the sampling is random, any two draws from the population are independent of each other. Random Sampling and the Sample Mean Sampling Theory triangleright Random Sampling and the Sample Mean Sampling Distribution Properties of the Sample Average Large Sample Properties Estimation 5 / 27 square As { X 1 , . . ., X N } are all drawn from the same population then the marginal distribution of each draw are identical. Therefore, we refer to this sample as an identically and independently distributed (i.i.d) sample . square If the sampling is not independent then the sample is an identically distributed sample . Sampling Distribution Sampling Theory Random Sampling and the Sample Mean triangleright Sampling Distribution Properties of the Sample Average Large Sample Properties Estimation 6 / 27 square Because our sample is randomly chosen, then each sample is a random variable. This means that any function of the sample will also be a random variable. square The most obvious function of the sample that we are interested in is the sample average . square The sample average is defined as X = 1 N N summationdisplay i =1 X i . square As is the case for any random variable we are interested in knowing the mean, variance and distribution of the sample average Properties of the Sample Average Sampling Theory Random Sampling and the Sample Mean Sampling Distribution triangleright Properties of the Sample Average Large Sample Properties Estimation 7 / 27 square Let { X 1 , . . . , X N } be an identically and independently distributed sample from a distribution with mean μ and variance σ 2 ....
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lect4_2010 - 1 27 Introduction to Econometrics Econ 322...

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