Probability describes a world you already know; inference asks the inverse question a desk actually faces: given a sample of returns, defaults, or factor exposures, what can you say about the unknown parameters that generated them? This topic builds estimation quality (bias, variance, MSE), maximum likelihood, confidence intervals and hypothesis tests, and simple linear regression as the bridge into econometrics. It sits on Probability foundations and assumes the primer's basic statistics as a floor, not a ceiling.
By the end of this note you should be able to:
- compare estimators by bias, variance and MSE, and compute an MLE a quant actually uses;
- construct large-sample intervals and run a mean-return test without treating a -value as a trading signal;
- fit and diagnose a simple linear regression of returns on a factor, reading , residuals and .
In this lesson
- Contents
- The big picture
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