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class03_14 - 1.017/1.010 Class 14 Estimation Estimating...

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Estimation Estimating Distributional Properties We can use random samples to estimatethe unknown properties of random variable x . These may be: 1. Distributional parameters , such as the lower and upper limits of a uniform distribution ( a and b ) 2. Other distributional properties such as the mean , variance , 90 th percentile value, etc. Parametric statistics assumes that the form of the x distribution of x is known. Nonparametric statistics makes no assumptions about distribution of x . Estimators An Estimator (or a statistic ) a is a function used to derive an estimate of the unknown distributional property a from a random sample x ) ,..., , ( ˆ 2 1 N x x x a ˆ 1 , x 2 ,..., x N ) ,..., , ( ˆ ˆ 2 1 N x x x a a = Example: Suppose we want to estimate from the random sample x 1 , x 2 ,..., x N the mean of F x ( x ) . A possible choice for the estimator is the sample mean m x . Then: a = E [ x ] = = = = N i i x N N a 1 2 1 1 ) ,..., , ( ˆ ˆ x m x x x a How do we know if this is a “good” estimator? Properties of Good Estimates
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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class03_14 - 1.017/1.010 Class 14 Estimation Estimating...

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