1 consider the data in example 86 find the plug-in, Ask an Expert

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1. Consider the data in Example 8.6. Find the plug-in estimate of the correlation coe?cient. Estimate the standard error using the bootstrap. Find a 95 percent con?dence interval using the Normal, pivotal, and percentile methods.

2. (Computer Experiment.) Conduct a simulation to compare the various bootstrap con?dence interval methods. Let n = 50 and let T (F ) =
( (x - µ)3dF (x)/σ3 be the skewness. Draw Y1,..., Yn ∼ N (0, 1) and set Xi = eYi , i = 1,..., n. Construct the three types of bootstrap 95 percent intervals for T (F ) from the data X1,..., Xn. Repeat this whole thing many times and estimate the true coverage of the three intervals.

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Category:- Statistics and Probability
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