Preface to First Edition - lib

SUMMARY 155R> layout(matrix(1:2, ncol = 2))R> bootplot(bootpara, 2, main = expression(mu[1]))R> bootplot(bootpara, 3, main = expression(mu[2]))µ 1µ 2Density0.0 0.2 0.4 0.6( ● )Density0.0 0.2 0.4 0.6 0.8( ● )52 54 5678 79 80 81 82N = 1000 Bandwidth = 0.1489N = 1000 Bandwidth = 0.111Figure 8.8Bootstrap distribution and confidence intervals for the mean estimatesof a two-component mixture for the geyser data.8.4 SummaryHistograms and scatterplots are frequently used to give graphical representationsof univariate and bivariate data. But both can often be improved andmade more helpful by adding some form of density estimate. For scatterplotsin particular, adding a contour plot of the estimated bivariate density can beparticularly useful in aiding in the identification of clusters, gaps and outliers.ExercisesEx. 8.1 The data shown in Table 8.3 are the velocities of 82 galaxies fromsix well-separated conic sections of space (Postman et al., 1986, Roeder,1990). The data are intended to shed light on whether or not the observableuniverse contains superclusters of galaxies surrounded by large voids. Theevidence for the existence of superclusters would be the multimodality ofthe distribution of velocities. Construct a histogram of the data and add avariety of kernel estimates of the density function. What do you concludeabout the possible existence of superclusters of galaxies?© 2010 by Taylor and Francis Group, LLC