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Q: After building the following model, show the efficiency of the model through sample sizes (20,50,100) and frequency 5000 through the attached table.
y= tiwi + Bij Xij +ei , i=1,2,…,n , j=1,2,3 , ei=(z1+z2)/2 ,
z1,z2 is box-Muller (mu=5,siqm=0.5), initial Bij is ols methods
𝑋𝑖𝑗= √(1−𝑟2) 𝑍𝑖𝑗+𝑟 𝑍𝑖𝑗 , r=0.75 , Zij ~ Normal
𝑤𝑖= {1 𝑖𝑓 𝑢𝑖≤ 0.5
0 𝑖𝑓 𝑢𝑖>0.5 𝑏̂=(𝑥′𝑤̂𝑥)−1(𝑥′𝑤̂𝑧̂)
𝑝=(e^𝐵𝑖𝑗𝑋𝑖/1+e^𝐵𝑖𝑗𝑋𝑖𝑗) 𝑞=1−𝑝 ,𝑝𝑞=𝑝𝑞 𝑤̂= 𝑑𝑖𝑎𝑔 (𝑝𝑞)
𝑧̂=log(𝑝)+ (𝑤−𝑝/𝑝𝑞)
س 2: بعد بناء النموذج التالي بين كفاءة النموذج من خلال حجوم العينات (20،50،100) والتكرار 5000 من خلال الجدول المرفق. (20 درجة) y= Bij Xij tei i=1,2,...,n.j=1,2,3, ei-(z1+z2)/2. z1,z2 is box-Muller (p=5.0-0.5), initial Bij is ols methods Xij = 1 - ) = , , Zij - Normal از 21 0.75=zij +r Zij r (32 - 1) 1if ui < 0.5 (0 if ul > 0.5 b = (x wix) -1 (xwt 2) wi = (BijXt ج p ) = ( ) q = 1-p, W = diag (pq) BijX و 14 2 = log(p) + -p PQ n=20 n=50) Best p=100) repa500 BO B1 B2 B3 Mse