Tutorial 91. Suppose we need to estimate a varying coefficient modelY=a0(x1) +a1(x2)x3+εwith sample (xi1, ...,xi3, Yi), i= 1, ..., n. Using cubic spline to approximateak(z).(a) write the expression for the estimator ofa1(z)(b) find the 95% confidence band fora1(x).2. Suppose we have ((data set), using one knott1= 0.5 for bothx1andx2, fit theabove model in question 1.3. Suppose we have data (xi, yi), i= 1, ..., nand need to estimateg(x) =E(yi|xi=x).LetY= (y1, ..., yn)and the fitted value ofYbeˆY. Show that both kernel smoothing(NW estimator and local linear kernel estimator) and polynomial splines methods have
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Trigraph, Polynomial interpolation, Kernel density estimation