Setting

• We have models $\mathcal{M}_1, …, \mathcal{M}_k$.
• There are $2n$ data points
• Split the data randomly into two: $D = (Y_1, …, Y_n)$ and $T = (Y^_1,…,Y^_n)$.

Definition 1

A random variable $X$ with mean $\mu = E[X]$ is sub-Gaussian if there is a positive number $\sigma$ such that

$$E[e^{\lambda (X - \mu)}] \le e^{\frac{\sigma^2 \lambda^2}{2}}$$

Step 1:

• Find MLE $\hat{\theta}_j$ using $D$.

(WIP)

Reference

AIC,BIC,Cross-Validation:

• http://www.stat.cmu.edu/~larry/=stat705/Lecture16.pdf

Concentration inequalities:

• https://www.stat.berkeley.edu/~mjwain/stat210b/Chap2_TailBounds_Jan22_2015.pdf