All simulators
Estimator Race: Bias, Variance & MSE
Mean, median and a shrinkage estimator compete across repeated samples.
Day 8: Estimators: Bias, Variance, MSE & ConsistencySample meanSample median0.90 × mean
| estimator | bias | variance | MSE |
|---|---|---|---|
| Sample mean | 0.048 | 3.847 | 3.849 |
| Sample median | 0.050 | 6.027 | 6.029 |
| 0.90 × mean | -0.156 | 3.116 | 3.141 |
Sample mean
Sample median
0.90 × mean
Solid = variance, light = bias². Lowest MSE: 0.90 × mean.
3,000 repeated samples per setting. With normal data the mean wins among unbiased estimators; with heavy tails (t₃) the median can beat it. Shrinkage wins when the truth is near zero.