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Dr. Hackney STA Solutions pg 195

# Dr. Hackney STA Solutions pg 195 -...

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Second Edition 12-5 12 . 29 The argument for the median is a special case of Example 12 . 4 . 3, where we take x i = 1 so σ 2 x = 1. The asymptotic distribution is given in (12 . 4 . 5) which, for σ 2 x = 1, agrees with Example 10 . 2 . 3. 12 . 31 The LAD estimates, from Example 12 . 4 . 2 are ˜ α = 18 . 59 and ˜ β = - . 89. Here is Mathematica code to bootstrap the standard deviations. (Mathematica is probably not the best choice here, as it is somewhat slow. Also, the minimization seemed a bit delicate, and worked better when done iteratively.) Sad is the sum of the absolute deviations, which is minimized iteratively in bmin and amin. The residuals are bootstrapped by generating random indices u from the discrete uniform distribution on the integers 1 to 23. 1 . First enter data and initialize Needs["Statistics‘Master‘"] Clear[a,b,r,u] a0=18.59;b0=-.89;aboot=a0;bboot=b0; y0={1,1.2,1.1,1.4,2.3,1.7,1.7,2.4,2.1,2.1,1.2,2.3,1.9,2.4,
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Unformatted text preview: 2.6,2.9,4,3.3,3,3.4,2.9,1.9,3.9}; x0={20,19.6,19.6,19.4,18.4,19,19,18.3,18.2,18.6,19.2,18.2, 18.7,18.5,18,17.4,16.5,17.2,17.3,17.8,17.3,18.4,16.9}; model=a0+b0*x0; r=y0-model; u:=Random[DiscreteUniformDistribution[23]] Sad[a_,b_]:=Mean[Abs[model+rstar-(a+b*x0)]] bmin[a_]:=FindMinimum[Sad[a,b],{b,{.5,1.5}}] amin:=FindMinimum[Sad[a,b/.bmin[a][[2]]],{a,{16,19}}] 2 . Here is the actual bootstrap. The vectors aboot and bboot contain the bootstrapped values. B=500; Do[ rstar=Table[r[[u]],{i,1,23}]; astar=a/.amin[[2]]; bstar=b/.bmin[astar][[2]]; aboot=Flatten[{aboot,astar}]; bboot=Flatten[{bboot,bstar}], {i,1,B}] 3 . Summary Statistics Mean[aboot] StandardDeviation[aboot] Mean[bboot] StandardDeviation[bboot] 4 . The results are Intercept: Mean 18 . 66, SD . 923 Slope: Mean-. 893, SD . 050....
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