Algorithm 1 Parameter Cascading Method

Outer Level of Optimization - Estimate θ(w) by minimizing H {θ(w)} Initialize θ(w) = θ(0)(w). Inner Level of Optimization - Estimate g(x, w) by minimizing J {α|θ(w)} Initialize α = α(0). Update α(i+1) = α(i) – {(d2 J) / (dαdαT)}−1(dJ/dα) until convergence. Obtain the estimate ĝ{x, w, θ(w)} = bT(x)Φ(w)α̂{θ(w)}. Update c(j+1) = c(j) – {(d2H)/(dcdcT)}−1(dH/dc) until convergence. Obtain the estimate for the varying coefficients: ${\widehat{\theta }}_k(w)={\mathit{\phi }}_k^{\mathrm{T}}(w){\widehat{\mathbf{c}}}_k$ and θ̂(w) = {θ̂1(w),…, θ̂m(w)}T.