plsim.MAVE {PLSiMCpp}

Minimum Average Variance Estimation

Description

MAVE (Minimum Average Variance Estimation), proposed by Xia et al. (2006) to estimate parameters in PLSiM

Y=\eta(Z^T\alpha)+X^T\beta+\epsilon.

Usage

plsim.MAVE(...)

## S3 method for class 'formula'
plsim.MAVE(formula, data, ...)

## Default S3 method:
plsim.MAVE(xdat=NULL, zdat, ydat, h=NULL, zeta_i=NULL, maxStep=100,
tol=1e-8, iniMethods="MAVE_ini", ParmaSelMethod="SimpleValidation", TestRatio=0.1, 
K = 3, seed=0, verbose=TRUE, ...)

Arguments

...

additional arguments.

formula

a symbolic description of the model to be fitted.

data

an optional data frame, list or environment containing the variables in the model.

xdat

input matrix (linear covariates). The model reduces to a single index model when x is NULL.

zdat

input matrix (nonlinear covariates). z should not be NULL.

ydat

input vector (response variable).

h

a numerical value or a vector for bandwidth. If h is NULL, a default vector c(0.01,0.02,0.05,0.1,0.5) will be given. plsim.bw is employed to select the optimal bandwidth when h is a vector or NULL.

zeta_i

initial coefficients, optional (default: NULL). It could be obtained by the function plsim.ini. zeta_i[1:ncol(z)] is the initial coefficient vector \alpha_0, and zeta_i[(ncol(z)+1):(ncol(z)+ncol(x))] is the initial coefficient vector \beta_0.

maxStep

the maximum iterations, default: 100.

tol

convergence tolerance, default: 1e-8.

iniMethods

string, optional (default: "SimpleValidation").

ParmaSelMethod

the parameter for the function plsim.bw.

TestRatio

the parameter for the function plsim.bw.

K

the parameter for the function plsim.bw.

seed

int, default: 0.

verbose

bool, default: TRUE. Enable verbose output.

Value

eta

estimated non-parametric part \hat{\eta}(Z^T{\hat{\alpha} }).

zeta

estimated coefficients. zeta[1:ncol(z)] is \hat{\alpha}, and zeta[(ncol(z)+1):(ncol(z)+ncol(x))] is \hat{\beta}.

data

data information including x, z, y, bandwidth h, initial coefficients zetaini and iteration step MaxStep.

y_hat

y's estimates.

mse

mean squares erros between y and y_hat.

variance

variance of y_hat.

r_square

multiple correlation coefficient.

Z_alpha

Z^T{\hat{\alpha}}.

References

Y. Xia, W. Härdle. Semi-parametric estimation of partially linear single-index models. Journal of Multivariate Analysis, 2006, 97(5): 1162-1184.

Examples

# EXAMPLE 1 (INTERFACE=FORMULA)
# To estimate parameters in partially linear single-index model using MAVE.

n = 30
sigma = 0.1

alpha = matrix(1,2,1)
alpha = alpha/norm(alpha,"2")

beta = matrix(4,1,1)

x = matrix(1,n,1)
z = matrix(runif(n*2),n,2)
y = 4*((z%*%alpha-1/sqrt(2))^2) + x%*%beta + sigma*matrix(rnorm(n),n,1)

fit = plsim.MAVE(y~x|z, h=0.1)

# EXAMPLE 2 (INTERFACE=DATA FRAME)
# To estimate parameters in partially linear single-index model using MAVE.

n = 30
sigma = 0.1

alpha = matrix(1,2,1)
alpha = alpha/norm(alpha,"2")
beta = matrix(4,1,1)

x = rep(1,n)
z1 = runif(n)
z2 = runif(n) 
X = data.frame(x)
Z = data.frame(z1,z2)

x = data.matrix(X)
z = data.matrix(Z)
y = 4*((z%*%alpha-1/sqrt(2))^2) + x%*%beta + sigma*matrix(rnorm(n),n,1)

fit = plsim.MAVE(xdat=X, zdat=Z, ydat=y, h=0.1)