plsim.npTest {PLSiMCpp}

Testing nonparametric component

Description

Study the hypothesis test:

H_0:\eta(u) = \theta_0+\theta_1u \ \mbox{ versus }\quad H_1:\ \eta(u)\ne \theta_0 + \theta_1u \ \mbox{for \ some \ } u

where \theta_0 and \theta_1 are unknown constant parameters.

Usage

plsim.npTest(fit)

Arguments

fit

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

Value

A list with class "htest" containing the following components

statistic

the value of the test statistic.

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)

res_npTest_plsimest = plsim.npTest(fit_plsimest)

# 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)

res_npTest_plsim = plsim.npTest(fit_plsim)