Sequential Variable Selection Using Cressie-Read \(\phi\)-Divergence Statistical Tests: Application to Small Samples of Light Vehicle Drivers

Abstract

We consider a sequence of matrices \((\bm{X},\bm{y})_{1},\cdots,(\bm{X},\bm{y})_ {N}\) \((N \in \mathbb{N}^{*})\) of dimensions \(n \times (Q +1)\) \((n >1, Q \geq 1 )\) consisting of nominal variables, where \(\bm{X}\) is an \(n \times Q\) matrix of explanatory variables and \(\bm{y}\)is an \(n \times 1) response variable. By combining the family of measures called "power divergence" and independence tests in contingency tables with small sample sizes, we construct a sequential selection process for \(X_{q}(q,\cdots,Q)\) based on sequences of independent random vectors, and we establish their asymptotic distributions. Applied to small random samples drawn from the database of road accidents involving light vehicle drivers in metropolitan France between 2005 and 2018, we show that factors such as location, road category, driver age, lighting conditions, and the main manoeuvre before the accident have a fairly frequent impact on the severity of road accidents involving drivers.