plsim.bw: select bandwidth

In PLSiMCpp: Methods for Partial Linear Single Index Model

select bandwidth

Description

Select bandwidth for methods, including MAVE, Profile Least Squares Estimator and Penalized Profile Least Squares Estimator by cross validation or simple validation.

Usage

plsim.bw(...)

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

## Default S3 method:
plsim.bw(xdat, zdat, ydat, zeta_i=NULL, bandwidthList=NULL, 
ParmaSelMethod="CrossValidation", K=5, TestRatio=0.1, TargetMethod='plsimest',
lambda=NULL, l1_ratio=NULL, VarSelMethod = "SCAD", MaxStep = 1L, 
verbose=FALSE, seed=0, ...)

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).
bandwidthList	vector, candidate bandwidths.
TargetMethod	string, optional (default: "plsimest"). target method to be selected bandwidth for, which could be "MAVE", "plsimest" and "plsim".
ParmaSelMethod	string, optional (default: "CrossValidation"). Method to select bandwidth, which could be Cross Validation ("CrossValidation") and Simple Validation ("SimpleValidation").
K	int, optional (default: 5). The number of folds for Cross Validation.
TestRatio	double, optional (default: 0.1). The ratio of test data for Simple Validation.
zeta_i	initial coefficients. 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.
lambda	the parameter for the function plsim.vs.soft, default: NULL.
l1_ratio	the parameter for the function plsim.vs.soft, default: NULL.
VarSelMethod	the parameter for the function plsim.vs.soft, default : "SCAD".
MaxStep	the parameter for the function plsim.vs.soft, default: 1.
verbose	the parameter for the function plsim.vs.soft, default: FALSE.
seed	int, default: 0.

Value

bandwidthBest	selected bandwidth
mse	mean square errors corresponding to the bandwidthList

Examples

# EXAMPLE 1 (INTERFACE=FORMULA)
# To select bandwidth by cross validation and simple validation. 

n = 50
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)

# Select bandwidth for profile least squares estimator by cross validation
res_plsimest_cross = plsim.bw(y~x|z,bandwidthList=c(0.02,0.04,0.06,0.08,0.10))

# Select bandwidth for profile least squares estimator by simple validation
res_plsimest_simple = plsim.bw(y~x|z,bandwidthList=c(0.02,0.04,0.06,0.08,0.10),
                            ParmaSelMethod="SimpleValidation")

# Select bandwidth for penalized profile least squares estimator by simple validation
res_plsim_simple = plsim.bw(y~x|z,bandwidthList=c(0.02,0.04,0.06,0.08,0.10),
                         ParmaSelMethod="SimpleValidation",TargetMethod="plsim",lambda=0.01)


# EXAMPLE 2 (INTERFACE=DATA FRAME)
# To select bandwidth by cross validation and simple validation. 

n = 50
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)

# Select bandwidth for profile least squares estimator by cross validation
res_plsimest_cross = plsim.bw(xdat=X,zdat=Z,ydat=y,bandwidthList=c(0.02,0.04,0.06,0.08,0.10))

# Select bandwidth for profile least squares estimator by simple validation
res_plsimest_simple = plsim.bw(xdat=X,zdat=Z,ydat=y,bandwidthList=c(0.02,0.04,0.06,0.08,0.10),
                            ParmaSelMethod="SimpleValidation")

# Select bandwidth for penalized profile least squares estimator by simple validation
res_plsim_simple = plsim.bw(xdat=X,zdat=Z,ydat=y,bandwidthList=c(0.02,0.04,0.06,0.08,0.10),
                         ParmaSelMethod="SimpleValidation",TargetMethod="plsim",lambda=0.01)
                                 

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