Suppose β^₁, β^₂, ... β^ₚ denote the estimator of regression coefficients in a linear regression obtained by minimizing
∑ᵢ₌₁ᵖ(yᵢ - ∑ⱼ₌₁ᵖβⱼxᵢⱼ)² subject to ∑ⱼ₌₁ᵖβⱼ² ≤ t for some t ≥ 0
Let β^ₗₛ denote the least square estimate of the coefficients with hat(β)LS,ⱼ ≠ 0 for atleast one j; j = 1, 2, ... p.
Which of the following must be true?
O For t > ∑ⱼ₌₁ᵖ β^ₗₛ²,∑ⱼ₌₁ᵖ β^ⱼ² > ∑ⱼ₌₁p βₗₛ,ⱼ
O For t > ∑ⱼ₌₁ᵖ β^ₗₛ², β^ⱼ = 0∀j
O For t > ∑ⱼ₌₁ᵖ β^ₗₛ², β^ⱼ = βₗₛ,ⱼ ∀j
O For t < ∑ⱼ₌₁ᵖ β^ₗₛ², ∑ⱼ₌₁p β^ⱼ² > ∑ⱼ₌₁p βₗₛ,ⱼ