R/np.gof.R

In PLRModels: Statistical Inference in Partial Linear Regression Models

np.gof <- function(data=data, m0=NULL, h.seq=NULL, w=NULL, estimator="NW", 
                   kernel="quadratic", time.series=FALSE, Tau.eps=NULL, h0=NULL, 
                   lag.max=50, p.max=3, q.max=3, ic="BIC", num.lb=10, alpha=0.05)
{
  
if (!is.matrix(data))  stop("data must be a matrix")
if (ncol(data) != 2)  stop("data must have 2 columns: y and t")

if ( (!is.null(m0)) && (!is.function(m0)) ) stop ("m0 must be a function")

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") ) {const1 <- 0.6; const2 <- 0.4337}
else if (kernel=="triweight") {const1 <- 0.8159; const2 <- 0.5879}
else if (kernel=="gaussian") {const1 <- 0.2821; const2 <- 0.1995}
else if (kernel=="uniform") {const1 <- 0.5; const2 <- 0.3333}
else 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(Tau.eps)) && (length(Tau.eps) !=1) ) stop ("Tau.eps must be an only value")
if ( (!is.null(Tau.eps)) && (!is.numeric(Tau.eps)) )  stop ("Tau.eps must be numeric") 

if ( (!is.null(h0)) && (length(h0) !=1) ) stop ("h0 must be an only value") 
if ( (!is.null(h0)) && (!is.numeric(h0)) )  stop ("h0 must be numeric")
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)
y <- data[,1]
t <- data[,2]

if (is.null(m0)) {m0 <- function(u) {0} }
f <- get("m0")


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

t1 <- intercept + slope*t
  
  
if (is.null(h0)) h0 <- 0.25/slope

if (is.null(h.seq)) h.seq <- (seq(0.05, 0.25, length.out=10))/slope
num.h <- length(h.seq)

if (is.null(w)) w <- (-intercept + c(0.1, 0.9))/slope



h0.2 <- slope*h0
h.seq.2 <- slope*h.seq
w.2 <- intercept + slope*w



M.est <- matrix(0,n,num.h)
y <- as.matrix(y)
    
M.est <- np.est(data=cbind(y, t1), newt=t1, h.seq=h.seq.2, estimator=estimator, kernel=kernel)
 
if (is.null(Tau.eps)) {

		M.est.0 <- np.est(data=cbind(y, t1), newt=t1, h.seq=h0.2, estimator=estimator, kernel=kernel)
    
		eps.0 <- y - M.est.0

		if (!time.series) Tau.eps.0 <- var(eps.0)  

		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.0 <- Var.Cov.sum[[1]]
		       pv.Box.test <- Var.Cov.sum[[2]]
		       pv.t.test <- Var.Cov.sum[[3]]
		       ar.ma <- Var.Cov.sum[[4]]
		}

}

	else Tau.eps.0 <- Tau.eps
  
weights <- 1:n
weights[((weights < n*w.2[1]+0.5) | (weights > n*w.2[2]+0.5))] <- 0
weights[weights != 0] <- 1
  
  
Q.m <- matrix(0,num.h,1)
Q.m.normalised <- matrix(0,num.h,1)
p.value <- matrix(0,num.h,1)
  

m.0 <- matrix (0,n,1)
m.0 <- f(t)


for (j in 1:num.h) {
    
   Q.m[j,] <- sum(weights*(M.est[,j] - m.0)^2)/n 
   mean.Q.m <-  Tau.eps.0 * const1 *(w.2[2]-w.2[1]) * (n*h.seq.2[j])^(-1)
   sd.Q.m <- (n^2*h.seq.2[j])^(-0.5) * sqrt(2*const2*((Tau.eps.0)^2) * (w.2[2]-w.2[1]))
    
   Q.m.normalised[j,] <- (Q.m[j,] - mean.Q.m)/sd.Q.m     
   p.value[j,] <- 1-pnorm(q=Q.m[j,], mean=mean.Q.m, sd=sd.Q.m)
    
} # for j
  
if ((is.null(Tau.eps)) && (time.series)) list(np.gof=data.frame(h.seq=h.seq, Q.m=Q.m, Q.m.normalised=Q.m.normalised, p.value=p.value), pv.Box.test=pv.Box.test, pv.t.test=pv.t.test, ar.ma=ar.ma)
else list(np.gof=data.frame(h.seq=h.seq, Q.m=Q.m, Q.m.normalised=Q.m.normalised, p.value=p.value))
  
}