Skip to content
Competitive Stats
Q33Section I (Objective (Q1–Q80))33 of 80

Bias–variance decomposition

Let T=T(x1,x2,…,xn)T=T(x_1,x_2,\dots,x_n) be an estimator of γ(θ)\gamma(\theta). Consider the following statements:

I. Eθ[T−γ(θ)]2=Eθ[T−Eθ(T)]2+[Eθ(T)−γ(θ)]2\mathbb{E}_\theta[T-\gamma(\theta)]^2 =\mathbb{E}_\theta[T-\mathbb{E}_\theta(T)]^2+[\mathbb{E}_\theta(T)-\gamma(\theta)]^2

II. The bias of TT is Eθ(T)−γ(θ)\mathbb{E}_\theta(T)-\gamma(\theta).

Options

Pick an option to check your answer. In a mock test a wrong answer here costs 0.83 mark.