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Estimating Optimal Transformations for Multiple Regression and Correlation
Abstract
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.
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Cites
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Cited by
Breiman, L. (1996) · Machine Learning · doi:10.1007/bf00058655 · Cited by 16,325
Self-citationEfron, B., & Tibshirani, R. (1986) · Statistical Science · doi:10.1214/ss/1177013815 · Cited by 6,033
Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author)
Breiman, L. (2001) · Statistical Science · doi:10.1214/ss/1009213726 · Cited by 4,340
Self-citationHoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999) · Statistical Science · doi:10.1214/ss/1009212519 · Cited by 4,118
Neural Networks and the Bias/Variance Dilemma
Geman, S., Bienenstock, E., & Doursat, R. (1992) · Neural Computation · doi:10.1162/neco.1992.4.1.1 · Cited by 3,578
Metadata
- Authors
- Breiman, L., & Friedman, J. H.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1985-09
- Volume
- 80
- Issue
- 391
- Pages
- 580-598
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2030748132
- Cited by
- 1,710
- References
- 2
- FWCI
- 21.95
- Type
- journal article
- Language
- en
- Open access
- closed
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