3. 8. Statistical simulations

2. specify the model and choose parameter values, ;
3. draw a random sample, , of size n from the specified distribution;
4. perform the statistical procedure - estimate parameters, compute test statistics;
5. repeat steps 2 and 3 many times to generate distributions of parameter estimates and test statistics;
6. use these distributions to compute bias or mean squared error (MSE) of parameter estimates or to compare the distribution of test statistics to the theoretical distribution.

After n simulations are run, the bias of a parameter estimate can be formulated as:

. (3.23)

is the parameter estimate from the ith simulation, and is the true value of the parameter. The MSE of the parameter estimate can be computed as

. (3.24)

After a distribution of test statistics is generated, it can be compared directly to the theoretical distribution. In doing so, the consistency of the two distributions can be determined.