Studying different approaches of estimating linear regression models, I recently came across quantile regression.
In the paper I was reading (http://www.econ.uiuc.edu/~roger/research/rq/rq.pdf) the author uses the following notation:
${\beta} \in \mathbb{R}^{p}$
What does the ${p}$ stand for in this context? I have not come across this notation before.
Thank you.
In quantile regression and more generally in statistics, $p$ often denotes that number of dependent variables (or covariates) in the data. The covariate vector $x_i$ in the paper you read is also $p$-dimensional with component $x_{ij}$ being the value of the $j$th covariate from the $i$th observation, where $i=1,\ldots,n$ and $j=1,\ldots,p$. Here, $n$ often means the number of observations in the data.