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plrm.ancova.R
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plrm.ancova.R
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plrm.ancova <- function(data=data, t=t, b.seq=NULL, h.seq=NULL, w=NULL, estimator="NW",
kernel="quadratic", time.series=FALSE, Var.Cov.eps=NULL,
Tau.eps=NULL, b0=NULL, h0=NULL, lag.max=50, p.max=3, q.max=3,
ic="BIC", num.lb=10, alpha=0.05)
{
if (!is.array(data)) stop("data must be an array")
if (ncol(data) < 2) stop("data must have at least 2 columns")
if (is.null(t)) stop("t must not be NULL")
if (sum(is.na(t)) != 0) stop("t must have numeric values")
if (any(t<0)) stop ("all elements in t must be positive")
if (length(t)!= nrow(data)) stop ("length(t) and nrow(data) must be equal")
if ( (!is.null(b.seq)) && (sum(is.na(b.seq)) != 0) ) stop ("b.seq must be numeric")
if ( (!is.null(b.seq)) && (any(b.seq<=0)) ) stop ("b.seq must contain one ore more positive values")
if ( (!is.null(h.seq)) && (sum(is.na(h.seq)) != 0) ) stop ("h.seq must be numeric")
if ( (!is.null(h.seq)) && (any(h.seq<=0)) ) stop ("h.seq must contain one ore more positive values")
if ( (!is.null(w)) && (sum(is.na(w) ) != 0) ) stop ("w must be numeric")
if ( (!is.null(w)) && (!is.vector(w)) ) stop ("w must be a vector")
if ( (!is.null(w)) && (length(w)!=2) ) stop("w must be a vector of length 2")
if ( (!is.null(w)) && (any(w<0)) ) stop ("w must contain two positive values")
if ( (!is.null(w)) && (w[1]>w[2]) ) stop("w[2] must be greater than w[1]")
if ((estimator != "NW") & (estimator != "LLP")) stop("estimator=NW or estimator=LLP is required")
if ((kernel != "quadratic") & (kernel != "Epanechnikov") & (kernel != "triweight") & (kernel != "gaussian") & (kernel != "uniform")) stop("kernel must be one of the following: quadratic, Epanechnikov, triweight, gaussian or uniform")
if (!is.logical(time.series)) stop("time.series must be logical")
if ( (!is.null(Var.Cov.eps)) && (sum(is.na(Var.Cov.eps)) != 0) ) stop("Var.Cov.eps must have numeric values")
if ( (!is.null(Var.Cov.eps)) && (!is.array(Var.Cov.eps)) ) stop("Var.Cov.eps must be an array")
if ( (!is.null(Var.Cov.eps)) && ( (ncol(Var.Cov.eps) != nrow(data)) | (nrow(Var.Cov.eps) != nrow(data)) | (dim(Var.Cov.eps)[3] != dim(data)[3]) ) ) stop("Var.Cov.eps must have dimension n x n x L")
if (!is.null(Var.Cov.eps)) {for (k in 1:(dim(Var.Cov.eps)[3]) ) if (any(t(Var.Cov.eps[,,k]) != Var.Cov.eps[,,k])) stop("Var.Cov.eps must be symmetric") }
if ( (!is.null(Tau.eps)) && (sum(is.na(Tau.eps)) != 0) ) stop("Tau.eps must have numeric values")
if ( (!is.null(Tau.eps)) && (!is.vector(Tau.eps)) ) stop("Tau.eps must be a vector")
if ( (!is.null(Tau.eps)) && (length(Tau.eps) != (ncol(data)-1)) ) stop ("Tau.eps must have length equals to ncol(data)-1")
if ( (!is.null(b0)) && (!is.numeric(b0)) ) stop ("b0 must be numeric")
if ( (!is.null(b0)) && (length(b0) !=1) ) stop ("b0 must be an only value")
if ( (!is.null(b0)) && (b0<=0) ) stop ("b0 must be a positive value")
if ( (!is.null(h0)) && (!is.numeric(h0)) ) stop ("h0 must be numeric")
if ( (!is.null(h0)) && (length(h0) !=1) ) stop ("h0 must be an only value")
if ( (!is.null(h0)) && (h0<=0) ) stop ("h0 must be a positive value")
if (is.null(lag.max)) stop ("lag.max must not be NULL")
if (length(lag.max) !=1) stop ("lag.max must be an only value")
if (!is.numeric(lag.max)) stop ("lag.max must be numeric")
if (lag.max<0) stop ("lag.max must be a positive value")
if (is.null(p.max)) stop ("p.max must not be NULL")
if (length(p.max) !=1) stop ("p.max must be an only value")
if (!is.numeric(p.max)) stop ("p.max must be numeric")
if (p.max<0) stop ("p.max must be a positive value")
if (is.null(q.max)) stop ("q.max must not be NULL")
if (length(q.max) !=1) stop ("q.max must be an only value")
if (!is.numeric(q.max)) stop ("q.max must be numeric")
if (q.max<0) stop ("q.max must be a positive value")
if ( (ic != "BIC") & (ic != "AIC") & (ic != "AICC") ) stop("ic=BIC or ic=AIC or ic=AICC is required")
if (is.null(num.lb)) stop ("num.lb must not be NULL")
if (length(num.lb) !=1) stop ("num.lb must be an only value")
if (!is.numeric(num.lb)) stop ("num.lb must be numeric")
if (num.lb<=0) stop ("num.lb must be a positive value")
if (is.null(alpha)) stop ("alpha must not be NULL")
if (length(alpha) !=1) stop ("alpha must be an only value")
if (!is.numeric(alpha)) stop ("alpha must be numeric")
if ( (alpha<0) | (alpha>1) ) stop ("alpha must be between 0 and 1")
n <- nrow(data)
p <- ncol(data)-1
L <- dim(data)[3]
if ( (is.null(h.seq)) & (!is.null(b.seq)) ) {h.seq <- b.seq}
if ( (is.null(b.seq)) & (!is.null(h.seq)) ) {b.seq <- h.seq}
if (length(b.seq) != length(h.seq)) stop("length(b.seq) and length(h.seq) must be equal")
if ( (is.null(h0)) & (!is.null(b0)) ) {h0 <- b0}
if ( (is.null(b0)) & (!is.null(h0)) ) {b0 <- h0}
dif <- t[2]-t[1]
for (i in 1:(n-1)) {
dist <- t[i+1]-t[i]
if (abs(dist - dif) < 2e-15) {}
else stop("t values must be equidistant")
}
x0 <- min(t)
x1 <- max(t)
y0 <- (1-0.5)/n
y1 <- (n-0.5)/n
slope <- (y1 - y0)/(x1-x0)
intercept <- y1-slope*x1
if (is.null(b.seq)) {b.seq <- (seq(0.05, 0.25, length.out=10))/slope; h.seq <- b.seq}
num.h <- length(h.seq)
num.b <- length(b.seq)
if (is.null(b0)) {b0 <- 0.25/slope; h0 <- b0}
if (is.null(w)) w <- (-intercept + c(0.1, 0.9))/slope
parametric.test <- matrix(1000,num.b,3)
dimnames(parametric.test) <- list(NULL, c("b", "Q", "p.v"))
nonparametric.test <- matrix(1000,num.h,5)
dimnames(nonparametric.test) <- list(NULL,c("b", "h", "Q", "Q.normalised", "p.v"))
if ((is.null(Var.Cov.eps)) | (is.null(Tau.eps))) {
# We build auxiliar residuals in order to estimate Var.Cov.eps and/or Tau.eps
eps.0 <- matrix(0,n,L)
for (k in 1:L) {
y.x.t <- cbind(data[,,k],t)
beta.est.0 <- plrm.beta(data=y.x.t, b.seq=b0, estimator=estimator, kernel=kernel)$BETA
y.0 <- data[,1,k]-data[,-1,k]%*%beta.est.0
m.0 <- np.est(data=cbind(y.0,t),newt=t, h.seq=h0, estimator=estimator, kernel=kernel)
eps.0[,k] <- y.0 - m.0
} # for
}
if (is.null(Var.Cov.eps)) {
v.c.eps <- TRUE
Var.Cov.eps <- array(0,c(n,n,L))
if (!time.series) {
for (k in 1:L) {
var.eps <- var(eps.0[,k])
var.eps <- as.numeric(var.eps)
Var.Cov.eps[,,k] <- diag(var.eps,n,n)
} # for
} # if
else {
for (k in 1:L) {
V.eps <- matrix(NA, n, n)
Var.Cov.mat <- var.cov.matrix(x=eps.0[,k], n=n, p.max=p.max, q.max=q.max, ic=ic, alpha=alpha, num.lb=num.lb)
V.eps <- Var.Cov.mat[[1]]
v.pv.Box.test <- Var.Cov.mat[[2]]
v.pv.t.test <- Var.Cov.mat[[3]]
v.ar.ma <- Var.Cov.mat[[4]]
Var.Cov.eps[,,k] <- V.eps
} # for
} # else
} # if
else v.c.eps <- FALSE
if (is.null(Tau.eps)) {
t.eps <- TRUE
if (!time.series) Tau.eps <- apply(eps.0, 2, var)
else {
Var.Cov.sum <- var.cov.sum(X=eps.0, lag.max=lag.max, p.max=p.max, q.max=q.max, ic=ic, alpha=alpha, num.lb=num.lb)
Tau.eps <- Var.Cov.sum[[1]]
t.pv.Box.test <- Var.Cov.sum[[2]]
t.pv.t.test <- Var.Cov.sum[[3]]
t.ar.ma <- Var.Cov.sum[[4]]
} # else
} # if
else t.eps <- FALSE
#####################################
# PARAMETRIC AND NON-PARAMETRIC TEST
#####################################
YY <- matrix(0,n,L)
WY <- matrix(0,n,1)
XX <- array(0,c(n,p,L))
WX <- matrix(0,n,L)
data_par1 <- array(0,c(n,p+1,L))
Y <- matrix(0,n,L)
beta.est <- matrix(0,p,1)
for (i in 1:num.b) {
for (k in 1:L) {
data1 <- cbind(data[,1,k],t)
WY <- np.est(data=data1,newt=t,h.seq=b.seq[i],estimator=estimator,kernel=kernel)
YY[,k] <- data[,1,k]-WY
data_par1[,1,k] <- YY[,k]
y.x.t <- cbind(data[,,k],t)
beta.est <- plrm.beta(data=y.x.t, b.seq=b.seq[i], estimator=estimator, kernel=kernel)$BETA
Y[,k] <- data[,1,k]-data[,-1,k]%*%beta.est
for (j in 1:p) {
data2 <- cbind(data[,j+1,k],t)
WX <- np.est(data=data2,newt=t,h.seq=b.seq[i],estimator=estimator,kernel=kernel)
XX[,j,k] <- data[,j+1,k]-WX
data_par1[,j+1,k] <- XX[,j,k]
} # for
} # for
# We test BETA_1= ... =BETA_L
par.test <- par.ancova(data=data_par1, time.series=time.series, Var.Cov.eps=Var.Cov.eps, p.max=p.max, q.max=q.max, ic=ic, alpha=alpha, num.lb=num.lb)
parametric.test[i,] <- c(b.seq[i], par.test$par.ancova$Q.beta, par.test$par.ancova$p.value)
# We test m_1=m_2=...=m_L
data_nopar2 <- matrix(c(Y,t),nrow=n)
np.test <- np.ancova(data=data_nopar2, h0=h0, h.seq=h.seq[i], w=w, estimator=estimator, kernel=kernel,
time.series=time.series, Tau.eps=Tau.eps, lag.max=lag.max, p.max=p.max, q.max=q.max, ic=ic, alpha=alpha, num.lb=num.lb)
nonparametric.test[i,] <- c(b.seq[i], h.seq[i], np.test$np.ancova$Q.m, np.test$np.ancova$Q.m.normalised, np.test$np.ancova$p.value)
} # for
parametric.test <- as.data.frame(parametric.test)
nonparametric.test <- as.data.frame(nonparametric.test)
if ( (v.c.eps) && (t.eps) && (time.series) ) list(parametric.test=parametric.test, nonparametric.test=nonparametric.test, pv.Box.test=v.pv.Box.test, pv.t.test=v.pv.t.test, v.ar.ma=v.ar.ma)
else if ( !(v.c.eps) && (t.eps) && (time.series) ) list(parametric.test=parametric.test, nonparametric.test=nonparametric.test, pv.Box.test=t.pv.Box.test, pv.t.test=t.pv.t.test, ar.ma=t.ar.ma)
else if ( (v.c.eps) && !(t.eps) && (time.series) ) list(parametric.test=parametric.test, nonparametric.test=nonparametric.test, pv.Box.test=v.pv.Box.test, pv.t.test=v.pv.t.test, ar.ma=v.ar.ma)
else list(parametric.test=parametric.test, nonparametric.test=nonparametric.test)
}