Section_2_v2 - Section 2 - Econ 140 GSI: Hedvig, Tarso and...

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Unformatted text preview: Section 2 - Econ 140 GSI: Hedvig, Tarso and Xiaoyu * 1 Review 1.1 Population versus sample Population : set of individuals, rms or any other entities that participate in one speci c experiment. Sample : subset of the population that we use to test something about the population. Simple random sample : subset drawn at random from a population, in a way that each entity is equally likely to be drawn. i.i.d. random variables : let X 1 ,...,X N be a collection of N random variables with the same p.d.f. and that are independent among themselves. We say that the random variables X 1 ,...,X N are independently and identically distributed ( i.i.d. ). 1.2 Estimation Estimator : function of a sample drawn randomly from a population. It is a random variable because of the randomness in selecting the sample. Estimate : numerical value generated by the estimator when we input data from a speci c sample on it. It is a nonrandom number . Properties of an estimator : Let c M be an estimator of the population parameter M . c M is an unbiased estimator of M if E c M = M Note : Bias = E c M- M c M is a consistent estimator of M if c M p M [i.e. if P h | c M- M | < i 1 as N ] Note : For unbiased estimators, we can check this property by showing that V ar c M as N Let f M be another estimator of M , and suppose that both f M and c M are unbiased. Then c M is said to be more e cient than f M if V ar c M < V ar f M . Note that e ciency is a property that depends on the set of estimators under consideration. Example : X = 1 N N i =1 X i is an estimator of X : Unbiased : E ( X ) = E 1 N N i =1 X i = 1 N N i =1 E ( X i ) = 1 N N i =1 X = 1 N ( N X ) = X * We thank Edson Severnini as our notes are based on his. All erros are ours. 1 Consistent : V ar ( X ) = V ar ( X ) N . So V ar ( X ) as N E cient among all linear unbiased estimators Best Linear Unbiased Estimator (BLUE ), where "best" means most e cient....
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This note was uploaded on 02/02/2012 for the course ECON 140 taught by Professor Duncan during the Spring '08 term at University of California, Berkeley.

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Section_2_v2 - Section 2 - Econ 140 GSI: Hedvig, Tarso and...

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