## Chapter 10. Simulation with Complex Data

Is an estimator biased in finite samples? Is an estimator consistent under departures from assumptions? Is the sampling variance under/overestimated under different assumptions? Does method *A* provide better properties than method *B* in terms of bias, precision, and so on? Is the size of a test correct (achieving nominal level of coverage under the null hypothesis)? Is the power of a test larger than for other tests?

All these questions can be answered by statistical simulation. Some of these questions have already been answered in Chapter 6, *Probability Theory Shown by Simulation* where the concept of bias, large numbers, and the central limit theorem was shown by simulation. We also saw Monte Carlo-based estimation of confidence intervals in Chapter 7, *Resampling Methods* (with the bootstrap, for example), and we have already discussed in detail the Monte-Carlo approach to testing in Chapter 8.

This chapter enhances previous chapters by introducing more...