HEC Montréal, Canada, May 2  4, 2011
2011 Optimization Days
HEC Montréal, Canada, 2 — 4 May 2011
WA1 Exposé magistral VI / Tutorial VI
May 4, 2011 10:30 AM – 12:10 PM
Location: Banque Scotia
Chaired by JeanFrancois Plante
1 Presentation

10:30 AM  12:10 PM
Monte Carlo Methods for Testing Statistical Hypotheses
In most applications of statistics, particularly in financial engineering, dynamic stochastic models are assumed to satisfy certain hypotheses, mainly related to their probabilistic distribution. For example, in time series, random error terms (innovations) are often assumed to be independent and/or have a distribution belonging to a specific family of distributions. The problem is then to test these statistical hypotheses. To make things worse, the asymptotic distribution of the tests statistics generally depends on unknown parameters, so it is impossible to construct tables of critical values. The solution to that problem is to use Monte Carlo methods to estimate the pvalue of test statistics. In this tutorial, I will focus on several interesting methods to estimate pvalues: bootstrap, parametric bootstrap and multipliers methodology. Examples of applications in actuarial science, econometrics, and financial engineering will be given.