d.boots {itdr}

Bootstrap Estimation for Dimension (d) of Sufficient Dimension Reduction Subspaces.

Description

The function “d.boots()” estimates the dimension of the central mean subspace and the central subspaces in regression.

Usage

d.boots(y,x,wx=0.1,wy=1,wh=1.5,B=500,var_plot=FALSE,space="mean"
                                        ,xdensity="normal",method="FM")

Arguments

y

The n-dimensional response vector.

x

The design matrix of the predictors with dimension n-by-p.

wx

(default 0.1). The tuning parameter for predictor variables.

wy

(default 1). The tuning parameter for the response variable.

wh

(default 1.5). The bandwidth of the kernel density estimation.

B

(default 500). Number of bootstrap samples.

var_plot

(default FALSE). If TRUE, it provides the dimension variability plot.

space

(default “mean”). The defalult is “mean” for the central mean subspace. Other option is “pdf” for estimating the central subspace.

xdensity

(default “normal”). Density function of predictor variables. Options are “normal” for multivariate normal distribution, “elliptic” for elliptical contoured distribution function, or “kernel” for estimating the distribution using kernel smoothing.

method

(default “FM”). The integral transformation method. “FM” for Fourier trans-formation method (Zhu and Zeng 2006), and “CM” for convolution transformation method (Zeng and Zhu 2010).

Value

The outputs includes a table of average bootstrap distances between two subspaceses for each candidate value of d and the estimated value for d.

dis_d

A table of average bootstrap distances for each candidate value of d.

d.hat

The estimated value for d.

plot

Provides the dimension variability plot if plot=TRUE.

Examples

# Use dataset available in itdr package
data(automobile)
head(automobile)
automobile.na <- na.omit(automobile)
# prepare response and predictor variables
auto_y <- log(automobile.na[, 26])
auto_xx <- automobile.na[, c(10, 11, 12, 13, 14, 17, 19, 20, 21, 22, 23, 24, 25)]
auto_x <- scale(auto_xx) # Standardize the predictors
# call to the d.boots() function with required arguments
d_est <- d.boots(auto_y, auto_x, var_plot = TRUE, space = "pdf", xdensity = "normal", method = "FM")
auto_d <- d_est$d.hat