The bias-variance trade-off in Thomson's multitaper estimator

Understand

At the heart of non-parametric spectral estimation, lies the dilemma known as the bias-variance trade-off: low biased estimators tend to have high variance and low variance estimators tend to have high bias.

• In 1982, Thomson introduced a multitaper method where this trade-off is made explicit by choosing a target bias resolution and obtaining a corresponding variance reduction.
• The method became the standard in many applications.
• Its favorable bias-variance trade-off is due to an empirical fact, conjectured by Thomson based on numerical evidence: assuming bandwidth W and N time domain observations, the average of the square of the first $K=\left\lfloor 2NW\right\rfloor$ Slepian functions approaches, as K grows, an ideal band-pass kernel for the interval [-W,W].