Probability and Statistics for Finance

Chapter 19. Hypothesis Testing

Thus far in this book, inference on some unknown parameter meant that we had no knowledge of its value and therefore we had to obtain an estimate. This could either be a single point estimate or an entire confidence interval. However, sometimes, one already has some idea of the value a parameter might have or used to have. Thus, it might not be important for a portfolio manager, risk manager, or financial manager to obtain a particular single value or range of values for the parameter, but instead gain sufficient information to conclude that the parameter more likely either belongs to a particular part of the parameter space or not. So, instead we need to obtain information to verify whether some assumption concerning the parameter can be supported or has to be rejected.

This brings us to the field of hypothesis testing. Next to parameter estimation that we covered in Chapters 17 and 18, it constitutes the other important part of statistical inference; that is, the procedure for gaining information about some parameter. To see its importance, consider, for example, a portfolio manager who might have in mind a historical value such as the expected value of the daily return of the portfolio under management and seeks to verify whether the expected value can be supported. It might be that if the parameter belongs to a particular set of values, the portfolio manager incurs extensive losses.

In this chapter, we learn how to perform hypothesis testing. To ...