Compare the effect of the Efron-Morris estimator on the baseball data in Section 8.3 with the effect of a James-Stein estimator which shrinks the values of π_i towards π₀ = 0.25 or equivalently shrinks the values of X_i towards µ, = 2√n sin^-1 √π₀.

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Table 8.1 Data for the baseball example. Name Si Ti mi Y₁ FEB Pi X₁ 0₁ 18 127 367 8.438 0.400 0.290 0.346 9.186 0.298 8.881 7.749 16 144 17 127 426 0.378 0.286 521 0.356 275 0.333 0.277 0.281 0.276 8.571 7.427 15 61 0.222 8.258 6.579 14 114 418 0.311 0.273 0.273 7.938 7.372 14 126 466 0.311 0.273 0.270 7.938 7.337 13 154 586 0.289 0.268 0.263 7.613 7.221 L. Alvardo 12 29 138 0.267 0.264 0.210 7.280 6.389 11 137 510 0.244 0.259 0.269 6.938 7.310 11 46 200 0.244 0.259 0.230 6.938 6.711 10 73 277 0.222 0.254 0.264 6.586 7.233 10 69 270 0.222 0.254 0.256 6.586 7.111 132 435 0.222 0.254 0.303 6.586 142 538 0.222 0.254 0.264 6.586 10 42 186 0.222 0.254 0.226 6.586 6.644 9 159 558 0.200 0.249 0.285 6.220 7.555 8 129 408 0.178 0.244 0.316 5.839 8.012 7 14 70 0.156 0.239 0.200 5.439 6.220 i 1 2 3 4 5 6 7 8 9 10 11 Clemente F. Robinson F. Howard Johnstone Berry Spencer Kessinger Santo Swoboda Unser Williams 12 13 Scott 14 Petrocelli 15 E Rodriguez 16 Campaneris 17 Munson 18 Alvis 10 10 7.827 7.239