plsim.MAVE: Minimum Average Variance Estimation

In PLSiMCpp: Methods for Partial Linear Single Index Model

Minimum Average Variance Estimation

Description

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

Y=η(Z^Tα)+X^Tβ+ε.

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 α_0, and zeta_i[(ncol(z)+1):(ncol(z)+ncol(x))] is the initial coefficient vector β_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{η}(Z^T{\hat{α} }).
zeta	estimated coefficients. zeta[1:ncol(z)] is \hat{α}, and zeta[(ncol(z)+1):(ncol(z)+ncol(x))] is \hat{β}.
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{α}}.

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)

PLSiMCpp documentation built on Sept. 24, 2022, 5:05 p.m.