Mean squared error
Mean squared error (MSE) measures estimator accuracy by summing two components: the estimator's variance and its squared bias. For an unbiased estimator, MSE equals variance alone.
Also known asMSE
See it move
The infographic is a tree diagram showing that MSE(θ̂) decomposes additively into two branches: Variance, which captures the scatter of repeated estimates around their own mean, and Bias², which measures the squared systematic offset of the estimator from the true parameter value. The equality MSE = Variance + Bias² means a single number summarises both dimensions of estimation quality. An estimator can be low-variance but highly biased, or unbiased but imprecise, and the MSE reveals the combined cost of both failings.
The formula
Variables
- Estimator of the true parameter θ
- True (unknown) population parameter
Defining form: the expected squared distance between the estimator and the true value.
Variables
- Variance of the estimator across repeated samples
- Systematic deviation of the estimator from the true parameter: E[θ̂] − θ
Bias-variance decomposition: for an unbiased estimator, Bias = 0 and MSE reduces to variance alone.