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Unformatted text preview: Chapter 8: Nonparametric Bootstrap Methods 4. Correlation and Regression bootstrap approach to making inferences about the correlation coefficient and the slope of a regression line Bivariate Bootstrap Sampling random sample ( X i , Y i ) i = 1 , . . ., n bivariate bootstrap sample: n n possible bootstrap samples bootstrap confidence interval for (a) draw a speified number of vibarate bootstrap samples of size n from the data with replacement (b) compute the bootstrap Pearson correlation coefficient r b for each bootstrap sample (c) a confidence interval from the distribution of the r b s. BCA method prefered / residual method has the undesirable property limits developed for the vibariate normal distribution Z = 1 2 ln parenleftbigg 1 + r 1- r parenrightbigg N parenleftbigg 1 2 ln parenleftbigg 1 + 1- parenrightbigg , 1 n- 3 parenrightbigg 100(1- )% confidence interval (1 + r ) e- c- (1- r ) (1 + r ) e- c + (1- r ) < < (1 + r ) e c- (1- r ) (1 + r ) e c + (1- r ) where c = 2 z / 2 / n- 3 1 Fixed- X Bootstrap Sampling regression model Y = h ( X ) + iid (0 , 2 ) when the X s are regarded as fixed, sample the errors and then add on an estimate of the mean function h ( X ) to get the bootstrap sample (a) hatwidest h ( x ) of the mean function h ( x ) (b) e i = Y i- hatwider h (...
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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.
- Spring '08