1985/09/01 by Leo Breiman, Jerome H. Friedman · 10 citations
Mathematics · #Advanced Statistical Methods and Models #Statistical and numerical algorithms #Statistical Methods and Inference
paper · doi:10.1080/01621459.1985.10478157
openalex publication_date 1985/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In regression analysis the response variable Y and the predictor variables X 1 …, Xp are often replaced by functions θ(Y) and Ø1(X 1), …, Ø p (Xp ). We discuss a procedure for estimating those functions θ and Ø1, …, Ø p that minimize e 2 = E[θ(Y) — Σ Ø j (Xj )]2/var[θ(Y)], given only a sample (yk , xk1 , …, xkp ), 1 ⩽ k ⩽ N and making minimal assumptions concerning the data distribution or the form of the solution functions. For the bivariate case, p = 1, θ and Ø satisfy ρ = p(θ, Ø) = maxθ,Øρ[θ(Y), Ø(X)], where ρ is the product moment correlation coefficient and ρ is the maximal correlation between X and Y. Our procedure thus also provides a method for estimating the maximal correlation between two variables.