Consider the linear model Yi = θ0 + x ⊤ i1θ1 + x ⊤ i2θ2 + ei , i ≥ 1. For testing H0 : θ1 = 0 vs. H1 : θ1 6= 0, the aligned rank statistic can be used. (Continuation). Consider the hypothesis H0 :...

Consider the linear model Yi = θ0 + x ⊤ i1θ1 + x ⊤ i2θ2 + ei , i ≥ 1. For testing H0 : θ1 = 0 vs. H1 : θ1 6= 0, the aligned rank statistic can be used.

(Continuation). Consider the hypothesis H0 : (θ0, θ ⊤ 1 ) ⊤ = 0 vs. H1 : (θ0, θ ⊤ 1 ) ⊤ 6= 0. For this testing, the signed-rank statistics are usable, but not the linear rank statistics.