hyperPara {itdr}

Bootstrap Estimation for Hyperparameters.

Description

The “hyperPara()” function estimates the hyperparameters that required in the Fourier transformation method.

Usage

hyperPara(y,x,d,wx=0.1,wy=1,wh=1.5,range=seq(0.1,1,by=.1),
xdensity="normal", B=500,space="mean", method="FM",hyper="wy")

Arguments

y

The n-dimensional response vector.

x

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

d

An integer specifying the dimension of the sufficient dimension reduction subspace.

wx

(default 0.1). Tuning parameter for the predictor variables.

wy

(default 1). Tuning parameter for the response variable.

wh

(default 1.5). Turning parameter for the bandwidth.

range

(default 0.1,0.2,...,1). A sequence of candidate values for the hyperparameter.

xdensity

Density function of predictor variables.

B

(default 500). Number of bootstrap samples.

space

(default “mean”). Specifies whether to estimate the central mean subspace (“mean”) or the central subspace (“pdf”).

method

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

hyper

(default “wy”). The hyperparameter to be estimated. Other choices are “wx” and “wy”.

Value

The outputs are a table of average bootstrap distances between two subspaces for each candidate value of the hyper parameter.

dis_h

A table of average bootstrap distances for each candidate value of the hyperparameter.

h.hat

The estimated hyperparameter.

References

Zeng P. and Zhu Y. (2010). An Integral Transform Method for Estimating the Central Mean and Central Subspaces. Journal of Multivariate Analysis. 101, 1, 271–290.

Zhu Y. and Zeng P. (2006). Fourier Methods for Estimating the Central Subspace and Central Mean Subspace in Regression. Journal of the American Statistical Association. 101, 476, 1638–1651.