Notation

Description Example Meaning
Lower case j \(\underline{x}^j\) Number of coordinate of vector \(\underline{x}\)
Lower case i \(\underline{x}_i = (x^1_i, \dots, x^p_i)'\) Identify one specific observation of a (column) vector of the explanatory variables
Parenthesis to apply power \(\left( x_i^j \right)^2\) Denotes the power of the \(j\)-th variable for the \(i\)-th observation
Caligraphic J \(x^\mathcal{J}\) Denotes a subset of indices
Negative Mathematical J \(x^{-\mathcal{J}}\) Removing the \(j\)-th coordinate
\(=z\) \(\underline{x}^{j|=z}=(x^1, \dots, x^{j-1}, z, x^{j+1}, \dots, x^p)'\) Replaces the \(j\)-th component of vector \(\underline{x}\) with \(z\)