QBUS3820 Lecture Notes - Lecture 6: Identity Matrix, Dividend Yield, Maximum A Posteriori Estimation

• School: University of Sydney
• Department: Business Analytics
• Course: QBUS3820
• Professor: Peter

Document Summary

Discipline of business analytics, the university of sydney business school. Lecture 6: linear model selection and regularisation: introduction, subset selection methods, regularisation methods, discussion. In this lecture we again focus the linear regression model. We move beyond ols to consider other estimation methods. The linear regression model is a special case based on a regression function of the form f (x) = 0 + 1x1 + 2x2 + . In the ols method, we select the coe cient values that minimise the residual sum of squares b ols = argmin. In the framework of the previous lecture, we can view ols as an empirical risk minimisation method. When the number of predictors, p, is large (e. g. comparable to n) ols has high variance and tends to over t. We can improve performance by setting some coe cients to zero or shrinking them. In other words, we will accept some bias in order reduce variance.