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Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics by Paolo Brandimarte

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Chapter Four

Estimation and Fitting

Before embarking in a computationally extensive Monte Carlo study, we should be reasonably confident that we are feeding our simulation tool with sensible input. In the previous chapter we have considered different families of models that can be used as the key ingredient to build a Monte Carlo simulator. Here we consider the quantitative side of the coin: After selecting a model structure, how should we estimate its parameters? Hence, we step into the domain of inferential statistics, whereby, given a sample of observed data, we engage in increasingly difficult tasks:

Finding point and interval estimates of basic moments like expected value and variance
Estimating the parameters of a possibly complicated probability distribution
Estimating the parameters of a time series model

The first task is typically associated with elementary concepts like confidence intervals, which may be somewhat dangerous and misleading for the newcomer. Computing a confidence interval for the mean of a normal population looks so easy that it is tempting to disregard the pitfalls involved. We will have more to say on this in Chapter 7, where we deal with output analysis. ...

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