Page 21 - Contributed Paper Session (CPS) - Volume 8

CPS2151 Sarah B. Balagbis
a. Choose m observations as “close” to each other as possible. This is
accomplished by fitting the model = + + +.. for all
1 1
0
2 2

observations and choosing m observations with the smallest
residuals.
1
b. Using the m observations from step (a), fit the model = +

0
1
1
+ + … and store the parameter estimates. Compute the
2 2
1 1
residuals of the remaining (n-m) observations and choose one
observation with the smallest residual to be added to the m
observations in step (a). This yield (m+1) observations.
c. Using the (m+1) observations from step (b), fit the model again and
store the parameter estimates. Compute the residual of the remaining
[n – (m+1)] observations and choose one observation with the
smallest residual.
d. Continue the process of estimating the parameters while Cook’s
distance for the newly entered observation is less than ε, otherwise
stop the process and get the series of parameter estimates you have
stored.
2. For each of the series of parameter estimates, compute a bootstrap
estimate:
a. Draw a simple random sample of size n with replacement.

1
̂
̂ ()
b. Compute the mean. = ∑

=1
c. Repeat (a) and (b) B times, where B is large.

1
̂ ()
d. Compute the bootstrap estimat ̂ = ∑ , and the standard
=1
1/2
1
̂
2
error ̂ = [ − 1 ∑( ̂ () − ) ]

=1
3. Given the bootstrap estimates of the parameters do the following:
̂
̂
̂
a. Compute = − − − − ⋯
2 2
0

1 1
b. For each i = 1, 2, …N, fit the model = (−1) + and store the

parameter estimates as , i = 1,…, N.

c. Compute the bootstrap estimate ̂ by following step 2 above.

1
4. Generate new series = − ̂ (−1) and iterate from step 1. Continue

the iteration until there is no substantial change in the values of the
parameter estimates
Simulation Studies
A simulation study is performed to illustrate and evaluate the performance
of the proposed estimation procedure. Seventy (70) panel points and eighty
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