. Author manuscript; available in PMC: 2016 Mar 31.

Published in final edited form as: Ann Stat. 2016 Mar 16;44(2):564–597. doi: 10.1214/15-AOS1377

Table 3.

Prediction errors of batting averages for the baseball data.

	ALL	Pitchers	NonPitchers
naive	1	1	1
Grand mean X̄₁.	0.852	0.127	0.378
Parametric EB-MM	0.593	0.129	0.387
Parametric EB-ML	0.902	0.117	0.398
Extended James-Stein	0.525	0.164	0.359
Nonparametric EB	0.508	0.212	0.372
Binomial mixture	0.588	0.156	0.314
Weighted least square (Null)	1.074	0.127	0.468
Weighted generalized MLE (Null)	0.306	0.173	0.326
Weighted least square (AB)	0.537	0.087	0.290
Weighted generalized MLE (AB)	0.301	0.141	0.261
Parametric URE θ̂^PG	0.515	0.105	0.278
Parametric URE θ̂^PM	0.421	0.105	0.276
Semi-parametric URE θ̂^SG	0.414	0.045	0.259
Semi-parametric URE θ̂^SM	0.422	0.041	0.273