$\newcommand{\0}{\mathbf 0}$$\newcommand{\one}{\mathbf 1}$In this post I’m going to work out the distribution of the area of a random parallelogram formed…
$\newcommand{\e}{\varepsilon}$$\newcommand{\one}{\mathbf 1}$Suppose I have collected data $X \in \mathbb R^{n\times p}$ ($n \geq p$ and $X$ is full column rank…
$\newcommand{\X}{\mathcal X}$$\newcommand{\dl}{\,\text d\lambda}$$\newcommand{\dx}{\,\text dx}$$\newcommand{\one}{\mathbf 1}$I’m going to take a look at functional linear regression, where I’ll find the best linear…
$\newcommand{\bern}{\text{Bern}}$$\newcommand{\vp}{\varphi}$$\newcommand{\e}{\varepsilon}$$\newcommand{\P}{\mathcal P}$$\newcommand{\Cov}{\text{Cov}}$$\newcommand{\E}{\text{E}}$$\newcommand{\one}{\mathbf 1}$$\newcommand{\s}{\mathbf s}$$\newcommand{\Disc}{\text{Disc}}$In this post I’m going to explore correlations between finitely-supported discrete variables. Bernoulli case I’ll begin with…
$\newcommand{\hb}{\hat\beta}$$\newcommand{\hbl}{\hat\beta_\lambda}$$\newcommand{\tb}{\tilde \beta}$$\newcommand{\L}{\mathcal L}$$\newcommand{\l}{\lambda}$$\newcommand{\e}{\varepsilon}$$\newcommand{\0}{\mathbf 0}$$\newcommand{\Lam}{\Lambda}$$\newcommand{\g}{\gamma}$$\newcommand{\D}{\mathcal D}$$\newcommand{\ht}{\hat\theta}$$\newcommand{\a}{\alpha}$In this post I’m going to explore ridge regression as a constrained optimization, and I’ll do…
$\newcommand{\e}{\varepsilon}$$\newcommand{\1}{\mathbf 1}$$\newcommand{\one}{\mathbf 1}$$\newcommand{\0}{\mathbf 0}$In this post I’m going to work with simple linear regression in matrix form. In most places…
In this post I want to take a look at interpolation with a single polynomial. I’ll prove the existence and…
$\newcommand{\I}{\mathcal I}$$\newcommand{\N}{\mathbb N}$$\newcommand{\Q}{\mathbb Q}$$\newcommand{\R}{\mathbb R}$In this post I’m going to explore partitioning the unit interval $\I := [0,1]$ into uncountably…
$\newcommand{\F}{\mathscr F}$$\newcommand{\a}{\alpha}$$\newcommand{\N}{\mathbb N}$$\newcommand{\w}{\omega}$$\newcommand{\E}{\mathcal E}$In this post I’m going to explore uncountable additivity of $\sigma$-finite measures a bit. Let $\mathcal M…
$\newcommand{\var}{\text{Var}}$$\newcommand{\cov}{\text{Cov}}$$\newcommand{\E}{\text{E}}$$\newcommand{\one}{\mathbf 1}$$\newcommand{\0}{\mathbf 0}$$\newcommand{\a}{\alpha}$$\newcommand{\l}{\lambda}$$\newcommand{\s}{\sigma}$$\newcommand{\e}{\varepsilon}$$\newcommand{\t}{\theta}$In this post I’m going to consider a linear model of the form $y = \mu\one + Z\a…