Case 2: Power plots for sample size T = 250, $ϕ=0$ and θ = 2.

Notes: This figure displays the rejection rates for testing the null hypothesis H₀: β = 0 versus the alternative H₁: $β≠0$ by the proposed RWB in Equation (14), IVX (IVX1 and IVX2), and IVX-based bootstrap (Wild and FWild) methods as the true value of β increases in Case 2. The horizontal dashed line denotes the 5% nominal size. Results are reported for different combinations of $ϕ=0$⁠, θ = 2, μ = 0 (a) and $μ=0.1$ (b). The average rejection rates are calculated over 10,000 replications with T = 250. RWB: Solid black; FWild: Dot-dashed blue; Wild: Yellow dashed; IVX1: Red short-dashed; IVX2: Green long-dashed.