note02 - Chapter 1: One-Sample Methods 1. Non-Parametric...

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Unformatted text preview: Chapter 1: One-Sample Methods 1. Non-Parametric Test of Hypothesis and CI for the Median Binomial Test (Sign Test) X 1 ,...,X n iid F ( x ) where F ( x ) is a continuous cdf . 5 : the population median Test H : . 5 = H a : . 5 > Define B = n summationdisplay i =1 i where i = braceleftbigg 1 if X i > 0 otherwise Uner H , Test H : . 5 = H a : . 5 > H : H a : Notice that under H , B is a distribution-free statistic over the class of all continuous distributions that have a median equal to . With large sample, by using normal approximation, Z B = B- . 5 n . 25 n > z 1- reject H at significant level Confidence Interval (Sign CI) 1- : the desired probability that the interval captures the median 1- Pr ( X ( a ) < . 5 < X ( b ) ) For large sample, obtain a and b by a- . 5 n . 25 n =- z 1- / 2 ( b- 1)- . 5 n . 25 n = z 1- / 2 rounding to the nearest integer. 1 2. Estimating the Population CDF and Percentiles CI for F ( x ) the empirical cdf: F ( x ) = 1 n n summationdisplay i =1 I { X i x } Note that E bracketleftBig F ( x ) bracketrightBig = F ( x ): unbiased estimator Y # of obs for which X i x = n F ( x ) = n i...
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This note was uploaded on 07/22/2011 for the course STA 4502 taught by Professor Staff during the Spring '08 term at University of Florida.

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note02 - Chapter 1: One-Sample Methods 1. Non-Parametric...

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