plsim.pTest {PLSiMCpp}

Testing Parametric Components

Description

Test whether some elements of \alpha and \beta are zero, that is,

H_0: \alpha_{i_1}=\cdots=\alpha_{i_k}=0 \ \mbox{ and } \beta_{j_1}=\cdots=\beta_{j_l}=0

versus

H_1: \mbox{not \ all }\ \alpha_{i_1},\cdots,\alpha_{i_k} \ \mbox{ and } \beta_{j_1}, \cdots,\beta_{j_l} \ \mbox{ are equal to }\ 0.

Usage

plsim.pTest(fit, parameterSelected = NULL, TargetMethod = "plsimest")

Arguments

fit

the result of function plsim.est or plsim.vs.soft.

parameterSelected

select some coefficients for testing, default: NULL.

TargetMethod

default: "plsim.est".

Value

A list with class "htest" containing the following components

statistic

the value of the test statistic.

parameter

the degree of freedom for the test

p.value

the p-value for the test

method

a character string indicating what type of test was performed

data.name

a character string giving the name of input

References

H. Liang, X. Liu, R. Li, C. L. Tsai. Estimation and testing for partially linear single-index models. Annals of statistics, 2010, 38(6): 3811.

Examples

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)

# Obtain parameters in PLSiM using Profile Least Squares Estimator
fit_plsimest = plsim.est(x, z, y)

# Test whether the parameters of parametric part estimated by plsimest
# are zero
res_pTest_plsimest = plsim.pTest(fit_plsimest)

# Test whether the second parameter of parametric part estimated by plsimest
# is zero
res_pTest_plsimest_ = plsim.pTest(fit_plsimest,parameterSelected = c(2))

# Obtain parameters in PLSiM using Penalized Profile Least Squares Estimator
# with lambda set as 0.01
fit_plsim = plsim.vs.soft(x,z,y,lambda = 0.01)

# Test whether the parameters of parametric part estimated by plsim are zero
res_pTest_plsim = plsim.pTest(fit_plsim,TargetMethod = "plsim")

# Test whether the second parameter of parametric part estimated by plsim is zero
res_pTest_plsim_ = plsim.pTest(fit_plsim,parameterSelected = c(2),TargetMethod = "plsim")