Description Usage Arguments Details Value Author(s) References See Also Examples
From samples {(Y_{ki}, X_{ki1}, ..., X_{kip}, t_i): i=1,...,n}, k=1,...,L, this routine tests the null hypotheses H0: β_1 = ... = β_L and H0: m_1 = ... = m_L, where:
β_k = (β_{k1},...,β_{kp})
is an unknown vector parameter;
m_k(.)
is a smooth but unknown function and
Y_{ki}= X_{ki1}*β_{k1} +...+ X_{kip}*β_{kp} + m(t_i) + ε_{ki}.
Fixed equally spaced design is considered for the "nonparametric" explanatory variable, t, and the random errors, ε_{ki}, are allowed to be time series. The test statistic used for testing H0: β_1 = ...= β_L derives from the asymptotic normality of an estimator of β_k (k=1,...,L) based on both ordinary least squares and kernel smoothing (this result giving a χ^2test). The test statistic used for testing H0: m_1 = ...= m_L derives from a CramervonMisestype functional based on different distances between nonparametric estimators of m_k (k=1,...,L).
1 2 3 4 5 
data 

t 
contains the values of the "nonparametric" explanatory (common) variable, t, for each model k (k=1, ..., L). 
b.seq 
the statistic test for H0: β_1 = ... = β_L is performed using each bandwidth in the vector 
h.seq 
the statistic test for H0: m_1 = ... = m_L is performed using each pair of bandwidths ( 
w 
support interval of the weigth function in the test statistic for H0: m_1 = ... = m_L. If 
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”. 
time.series 
it denotes whether the data are independent (FALSE) or if data is a time series (TRUE). The default is FALSE. 
Var.Cov.eps 

Tau.eps 

b0 
if 
h0 
if 
lag.max 
if 
p.max 
if 
q.max 
if 
ic 
if 
num.lb 
if 
alpha 
if 
A weight function (specifically, the indicator function 1_{[w[1] , w[2]]}) is introduced in the test statistic for testing H0: m_1 = ... = m_L to allow elimination (or at least significant reduction) of boundary effects from the estimate of m_k(t_i).
If Var.Cov.eps=NULL
and the routine is not able to suggest an approximation for Var.Cov.eps
, it warns the user with a message saying that the model could be not appropriate and then it shows the results. In order to construct Var.Cov.eps
, the procedure suggested in AneirosPerez and Vieu (2013) can be followed.
If Tau.eps=NULL
and the routine is not able to suggest an approximation for Tau.eps
, it warns the user with a message saying that the model could be not appropriate and then it shows the results. In order to construct Tau.eps
, the procedures suggested in AneirosPerez (2008) can be followed.
Expressions for the implemented statistic tests can be seen in (15) and (16) in AneirosPerez (2008).
A list with two dataframes:
parametric.test 
a dataframe containing the bandwidths, the statistics and the pvalues when one tests H0: β_1 = ...= β_L. 
nonparametric.test 
a dataframe containing the bandwidths b and h, the statistics, the normalised statistics and the pvalues when one tests H0: m_1 = ...= m_L. 
Moreover, if data
is a time series and Tau.eps
or Var.Cov.eps
are not especified:
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. 
ar.ma 
ARMA orders for the model fitted to the residuals. 
German Aneiros Perez [email protected]
Ana Lopez Cheda [email protected]
AneirosPerez, G. (2008) Semiparametric analysis of covariance under dependence conditions within each group. Aust. N. Z. J. Stat. 50, 97123.
AneirosPerez, G. and Vieu, P. (2013) Testing linearity in semiparametric functional data analysis. Comput. Stat. 28, 413434.
Other related functions are plrm.est
, par.ancova
and np.ancova
.
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 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78  # EXAMPLE 1: REAL DATA
data(barnacles1)
data < as.matrix(barnacles1)
data < diff(data, 12)
data < cbind(data,1:nrow(data))
data(barnacles2)
data2 < as.matrix(barnacles2)
data2 < diff(data2, 12)
data2 < cbind(data2,1:nrow(data2))
data3 < array(0, c(nrow(data),ncol(data)1,2))
data3[,,1] < data[,4]
data3[,,2] < data2[,4]
t < data[,4]
plrm.ancova(data=data3, t=t)
# EXAMPLE 2: SIMULATED DATA
## Example 2a: dependent data  true null hypotheses
set.seed(1234)
# We generate the data
n < 100
t < ((1:n)0.5)/n
beta < c(0.05, 0.01)
m1 < function(t) {0.25*t*(1t)}
f < m1(t)
x1 < matrix(rnorm(200,0,1), nrow=n)
sum1 < x1%*%beta
epsilon1 < arima.sim(list(order = c(1,0,0), ar=0.7), sd = 0.01, n = n)
y1 < sum1 + f + epsilon1
data1 < cbind(y1,x1)
x2 < matrix(rnorm(200,1,2), nrow=n)
sum2 < x2%*%beta
epsilon2 < arima.sim(list(order = c(0,0,1), ma=0.5), sd = 0.02, n = n)
y2 < sum2 + f + epsilon2
data2 < cbind(y2,x2)
data_eq < array(c(data1,data2), c(n,3,2))
# We apply the tests
plrm.ancova(data=data_eq, t=t, time.series=TRUE)
## Example 2b: dependent data  false null hypotheses
set.seed(1234)
# We generate the data
n < 100
t < ((1:n)0.5)/n
m3 < function(t) {0.25*t*(1t)}
m4 < function(t) {0.25*t*(1t)*0.75}
beta3 < c(0.05, 0.01)
beta4 < c(0.05, 0.02)
x3 < matrix(rnorm(200,0,1), nrow=n)
sum3 < x3%*%beta3
f3 < m3(t)
epsilon3 < arima.sim(list(order = c(1,0,0), ar=0.7), sd = 0.01, n = n)
y3 < sum3 + f3 + epsilon3
data3 < cbind(y3,x3)
x4 < matrix(rnorm(200,1,2), nrow=n)
sum4 < x4%*%beta4
f4 < m4(t)
epsilon4 < arima.sim(list(order = c(0,0,1), ma=0.5), sd = 0.02, n = n)
y4 < sum4 + f4 + epsilon4
data4 < cbind(y4,x4)
data_neq < array(c(data3,data4), c(n,3,2))
# We apply the tests
plrm.ancova(data=data_neq, t=t, time.series=TRUE)

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