plsim.bw {PLSiMCpp}

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 \alpha_0, and zeta_i[(ncol(z)+1):(ncol(z)+ncol(x))] is the initial coefficient vector \beta_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)