Confidence intervals estimation in partial linear regression models
Description
This routine obtains a confidence interval for the value a^T * β, by asymptotic distribution and bootstrap, {(Y_i, X_{i1}, ..., X_{ip}, t_i): i=1,...,n}, where:
a = (a_1,...,a_p)^T
is an unknown vector,
β = (β_1,...,β_p)^T
is an unknown vector parameter and
Y_i= X_{i1}*β_1 +...+ X_{ip}*β_p + m(t_i) + ε_i.
The nonparametric component, m, is a smooth but unknown function, and the random errors, ε_i, are allowed to be time series.
Usage
1 2 3 4 5 
Arguments
data 

seed 
the considered seed. 
CI 
method to obtain the confidence interval. It allows us to choose between: “AD” (asymptotic distribution), “B” (bootstrap) or “all” (both). The default is “AD”. 
B 
number of bootstrap replications. The default is 1000. 
N 
Truncation parameter used in the finite approximation of the MA(infinite) expression of ε. 
a 
Vector which, multiplied by 
b1 
the considered bandwidth to estimate the confidence interval by asymptotic distribution. If NULL (the default), it is obtained using crossvalidation. 
b2 
the considered bandwidth to estimate the confidence interval by bootstrap. If NULL (the default), it is obtained using crossvalidation. 
estimator 
allows us the choice between “NW” (NadarayaWatson) or “LLP” (Local Linear Polynomial). The default is “NW”. 
kernel 
allows us the choice between “gaussian”, “quadratic” (Epanechnikov kernel), “triweight” or “uniform” kernel. The default is “quadratic”. 
p.arima 
the considered p to fit the model ARMA(p,q). 
q.arima 
the considered q to fit the model ARMA(p,q). 
p.max 
if 
q.max 
if 
alpha 
1  
alpha2 
significance level used to check (if needed) the ARMA model fitted to the residuals. The default is 0.05. 
num.lb 
if 
ic 
if 
Var.Cov.eps 

Value
A list containing:
Bootstrap 
a dataframe containing 
AD 
a dataframe containing 
pv.Box.test 
pvalues of the LjungBox test for the model fitted to the residuals. 
pv.t.test 
pvalues of the t.test for the model fitted to the residuals. 
Author(s)
German Aneiros Perez ganeiros@udc.es
Ana Lopez Cheda ana.lopez.cheda@udc.es
References
Liang, H., Hardle, W., Sommerfeld, V. (2000) Bootstrap approximation in a partially linear regression model. Journal of Statistical Planning and Inference 91, 413426.
You, J., Zhou, X. (2005) Bootstrap of a semiparametric partially linear model with autoregressive errors. Statistica Sinica 15, 117133.
See Also
A related functions is par.ci
.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36  # EXAMPLE 1: REAL DATA
data(barnacles1)
data < as.matrix(barnacles1)
data < diff(data, 12)
data < cbind(data,1:nrow(data))
b.h < plrm.gcv(data)$bh.opt
b1 < b.h[1]
## Not run: plrm.ci(data, b1=b1, b2=b1, a=c(1,0), CI="all")
## Not run: plrm.ci(data, b1=b1, b2=b1, a=c(0,1), CI="all")
# EXAMPLE 2: SIMULATED DATA
## Example 2a: dependent data
set.seed(123)
# We generate the data
n < 100
t < ((1:n)0.5)/n
m < function(t) {t+0.5}
f < m(t)
beta < c(0.5, 2)
x < matrix(rnorm(200,0,3), nrow=n)
sum < x%*%beta
sum < as.matrix(sum)
eps < arima.sim(list(order = c(1,0,0), ar=0.7), sd = 0.1, n = n)
eps < as.matrix(eps)
y < sum + f + eps
data_plrmci < cbind(y,x,t)
## Not run: plrm.ci(data, a=c(1,0), CI="all")
## Not run: plrm.ci(data, a=c(0,1), CI="all")
