It creates objects of class edr to estimate the effective dimension regression (e.d.r) space. Several helper functions that require a edr object can then be applied to the output from this function.
edr(Y, X, H, K, method)
- A numeric vector representing the dependent variable (a response vector).
- A matrix representing the quantitative explanatory variables (bind by column).
- The chosen number of slices.
- The chosen dimension K.
- This character string specifies the method of fitting. The option includes "SIR-I", "SIR-II", and "SAVE".
We interested in the following semiparametric dimension reduction model proposed by Li (1991) y=f(b1'x,b2'x,...,bK'x,e) where the univariate response variable y is associated with the p-dimensional regressor p only through the reduced K-dimensional variable (b1'x,b2'x,...,bK'x) with K < p. The error term e is independent of x. The link function f and the b-vectors are unknown. We are interested in finding the linear subspace spanned by the K unknown b-vector, called the effective dimension reduction (e.d.r.) space. We focus on the SIR, SIR-II and SAVE methods to estimate the e.d.r space. The slicing step of these methods depends on the number H of slices. We propose with the function
criterionRkh a naive bootstrap estimation of the square trace correlation criterion to allow selection of an “optimal” number H of slices and simultaneously the corresponding suitable dimension K (number of the linear combination of x). After choosing an optimal couple (H,K) for the best estimation method (the square trace correlation criterion closest to one), the e.d.r space could be estimate with this function. Each method consists in a spectral decomposition of a matrix of interest. The eigenvectors of this matrix associated of the K largest eigenvalues are e.d.r directions.
edr returns an object that inherits from edr, with attributes:
- A matrix corresponding of the eigenvectors of the interest matrix
- The eigenvalues of the matrix of interest
- The chosen dimension.
- The chosen number of slices.
- Sample size.
- The dimension reduction method used.
- The matrix of the quantitative explanatories variables (bind by column).
- The numeric vector of the dependent variable (a response vector).
Liquet B. and Saracco, J., A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches. Revised paper.
Li, K.C. (1991). Sliced inverse regression for dimension reduction, with discussions. Journal of the American Statistical Association 86, 316-342.
Cook, R. D. and Weisberg, S. (1991). Discussion of “Sliced inverse regression”. Journal of the American Statistical Association, 86, 328-332.
set.seed(10) n <- 500 beta1 <- c(1,1,rep(0,8)) beta2 <- c(0,0,1,1,rep(0,6)) X <- rmvnorm(n,sigma=diag(1,10)) eps <- rnorm(n) Y <- (X%*%beta1)**2+(X%*%beta2)**2+eps ## Estimation of the trace square criterion ## grid.H <- c(2,5,10,15,20,30) ## res2 <- criterionRkh(Y,X,H=grid.H,B=50,method="SIR-II") ## summary(res2) ## plot(res2) ## Estimation of the e.d.r direction for K=2 and H=2 and SIR-II method edr2 <- edr(Y,X,H=2,K=2,method="SIR-II") summary(edr2) plot(edr2)
Documentation reproduced from package edrGraphicalTools, version 1.0. License: GPL (>= 2.0)