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3 Jun 2024: ψ(ρ)1 (β,τ. 2) =. pj=1. ( β. tj)ψ(tj ),. ψ(ρ)2 (β,τ. ... 2) =. pj=1. tj ψ(tj ) E[Tψ(T )], for T N(0, 1).

19 Jun 2024: xn,l. Set iteration counters tj,i = 0Set x̃j0 = rgmin. xj,1,.,xj,lE[f(xj,i;ξj,i0)], x̃0 = rgmin. ... j,i)tj,i = tj,i 1;. if nlτ divides (n︀j=1. l︀i=1. tj,i) then.

3 Jun 2024: 4): Q-Q plot of standardized residual:. tj (β̂) =Γ̂j β̂γ̂j. 1 β̂2. ... Robust adjusted profile score (RAPS). I Define standardized residual: tj (β,τ2) =. Γ̂j βγ̂j1 β2 τ2. I For some robust loss ρ (let ψ = ρ′), the RAPS equations

3 Jun 2024: 2 (Ti)iI (Tj)jInc;3 (Tj)jInc is mutually independent;. 4 (Ti)iI is PRDS on (Ti)iI0;. ... R(t) 1, 0 t 1. Further define. Vnc(t) :=jInc. 1{Tj t}, V̄nc(t) :=n (Vnc(t) 2).

3 Jun 2024: 4): Q-Q plot of standardized residual:. tj (β̂) =Γ̂j β̂γ̂j. 1 β̂2. ... Robust adjusted profile score (RAPS). I Define standardized residual: tj (β,τ2) =. Γ̂j βγ̂j1 β2 τ2. I For some robust loss ρ (let ψ = ρ′), the RAPS equations

25 Jun 2024: i1j =1. tij. (i1k=1. tikσj k j 1k=1. tj kσik. ), (A4). ... tij tj ktkσi〉. (A7). As above, the first sum vanishes except for = j.

29 May 2024: S. Adding thelines (. p (tj ti))((p tj) (p ti). )(A2). (p tj) (p ti) (MP)p ti (MP). ... Finally, if there exist j,k < isuch that tk = (tj ti), then v(tj) = v(tj ti) = 1 by induction hypothesis,and hence v(ti) = 1.

19 Jun 2024: Randomly initialize x1,1,x1,2,. ,xn,lSet iteration counters tj,i = 0Set x̃j0 = arg min. ... Draw random sample ξj,itj,ixj,i xj,i ηgj,it (xj,i)tj,i = tj,i 1;. if nlτ divides (nj=1.

3 Jun 2024: Robust adjusted profile score (RAPS). I Define standardized residual: tj (β,τ2) =. Γ̂j βγ̂j(σ2Yj τ. 2) β2σ2Xj. I For some robust loss function ρ, the RAPS are. ... ψ(ρ)1 (β,τ. 2) =. pj=1. ρ′(tj ). βtj,. ψ(ρ)2 (β,τ. 2) =. pj=1.

25 Jun 2024: Fij =〈xi1x. Tj1〉pθ〈eie. Tj. 〉pθ. (22). There is no reason to expect that this expression is zero for i 6= j, unless the outputs xi or the errorsei are ... Fij =(Wbi ΣW. bj. T)(Wai. T Σ̃1Waj. )=〈xi1x. Tj1〉pθ〈eie. Tj. 〉pθ.