What maximum likelihood estimation means
Question
Explain the idea behind maximum likelihood estimation of model parameters.
Short answer
Pick the parameters that make the observed data most probable. Write the joint density of the sample as a function of the parameters (the likelihood), usually take logs so independent observations add, and maximise analytically or numerically. In finance it is used, for example, to fit volatility from returns or GARCH parameters; under regularity conditions MLEs are consistent and asymptotically normal and efficient.
Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 12, p.61; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Maximum Likelihood Estimation: Score and Log-Likelihood
- Bias, Variance, and Mean Squared Error
- Populations, Samples, and Sampling Distributions
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