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# note16 - Chapter 8 Nonparametric Bootstrap Methods 4...

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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 ρ (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 + ρ 1 - ρ parenrightbigg , 1 n - 3 parenrightbigg 100(1 - α )% confidence interval (1 + r ) e - c - (1 - r ) (1 + r ) e - c + (1 - r ) < ρ < (1 + r ) e c - (1 - r ) (1 + r ) e c + (1 - r ) where c = 2 z α/ 2 / n - 3 1

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Fixed- X Bootstrap Sampling regression model Y = h ( X ) + ǫ ǫ iid (0 , σ 2 ) when the X ’s are regarded as fixed, sample the errors and then add
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