itdr (version 2.0.1)

d.boots: 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")

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.

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).

Examples

# \donttest{
# 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
# }