Nothing
R/gel.R
In gmm: Generalized Method of Moments and Generalized Empirical Likelihood
Defines functions
.vcovGel
.getImpProb
.thetf
evalGel
gel
getLamb
.CUE_lamPos2
.CUE_lamPos
.CUE_lam
.Wu2
.Wu
.getCgelLam
.rho
Documented in
evalGel
gel
getLamb
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# A copy of the GNU General Public License is available at
# http://www.r-project.org/Licenses/
.rho <- function(x, lamb, derive = 0, type = c("EL", "ET", "CUE", "HD", "ETEL", "ETHD",
"RCUE"), k = 1)
{
type <- match.arg(type)
if (type == "RCUE")
type <- "CUE"
gml <- x%*%c(lamb)*k
if (derive == 0)
{
if (type == "EL")
{
if (any(gml>=1))
stop("Computation of Lambda fails because NAs produced by log(1-gt*l)")
rhomat <- log(1 - gml)
}
if (type == "ET")
rhomat <- -exp(gml)
if (type == "CUE")
rhomat <- -gml -0.5*gml^2
if (type == "HD")
rhomat <- -2/(1-gml/2)
if (type == "ETEL")
{
w <- -exp(gml)
w <- w/sum(w)
rhomat <- -log(w*NROW(gml))
}
if (type == "ETHD")
{
w <- -exp(gml)
w <- w/sum(w)
rhomat <- (sqrt(w)-1/sqrt(NROW(gml)))^2
}
}
if (derive==1)
{
if (type == "EL")
rhomat <- -1/(1 - gml)
if (type == "ET")
rhomat <- -exp(gml)
if (type == "CUE")
rhomat <- -1 - gml
if (type == "HD")
rhomat <- -1/((1-gml/2)^2)
if (any(type == c("ETEL","ETHD")))
rhomat <- NULL
}
if (derive==2)
{
if (type == "EL")
rhomat <- -1/(1 - gml)^2
if (type == "ET")
rhomat <- -exp(gml)
if (type == "CUE")
rhomat <- -rep(1,nrow(x))
if (type == "HD")
rhomat <- -1/((1-gml/2)^3)
if (any(type == c("ETEL","ETHD")))
rhomat <- NULL
}
return(c(rhomat))
}
.getCgelLam <- function(gt, l0, type = c('EL', 'ET', 'CUE', "HD"),
method = c("nlminb", "optim", "constrOptim"),
control=list(), k = 1, alpha = 0.01)
{
type <- match.arg(type)
method <- match.arg(method)
fct <- function(l, X)
{
r1 <- colMeans(.rho(gt,l,derive=1,type=type,k=k)*X)
crossprod(r1) + alpha*crossprod(l)
}
Dfct <- function(l, X)
{
r2 <- .rho(X,l,derive=2,type=type,k=k)
r1 <- .rho(X,l,derive=1,type=type,k=k)
H <- t(X*r2)%*%X/nrow(X)
2*H%*%colMeans(r1*X) + 2*alpha*l
}
if (method == "nlminb")
res <- nlminb(l0, fct, Dfct, X = gt, control = control)
if (method == "optim")
res <- optim(l0, fct, Dfct, X = gt, method="BFGS", control = control)
if (method == "constrOptim")
{
ci <- -rep(1,nrow(gt))
res <- constrOptim(rep(0,ncol(gt)),fct,Dfct,-gt,ci,control=control,X=gt)
}
if (method == "optim")
{
conv <- list(convergence = res$convergence,
counts = res$counts, message = res$message)
} else {
conv <- list(convergence = res$convergence, counts = res$evaluations,
message = res$message)
}
return(list(lambda = res$par, convergence = conv,
obj = mean(.rho(gt,res$par, derive=0,type=type,k=k)) -
.rho(1,0, derive=0,type=type,k=k)))
}
.Wu <- function(gt, tol_lam = 1e-8, maxiterlam = 50, K=1)
{
u <- as.matrix(gt)
n=length(nrow(u))
M=rep(0,ncol(u))
dif=1
tol=tol_lam
k=0
while(dif>tol & k<=maxiterlam)
{
D1=t(u)%*%((1/(1+u%*%M))*rep(1,n))
DD=-t(u)%*%(c((1/(1+u%*%M)^2))*u)
D2=solve(DD,D1,tol=1e-40)
dif=max(abs(D2))
rule=1
while(rule>0)
{
rule=0
if(min(1+t(M-D2)%*%t(u))<=0) rule=rule+1
if(rule>0) D2=D2/2
}
M=M-D2
k=k+1
}
if(k>=maxiterlam)
{
M=rep(0,ncol(u))
conv = list(convergence=1)
} else {
conv = list(convergence=0)
}
return(list(lambda = c(-M), convergence = conv, obj =
mean(.rho(gt,-M,derive=0,type="EL",k=K))))
}
.Wu2 <- function(gt, tol_lam = 1e-8, maxiter = 50, K = 1)
{
gt <- as.matrix(gt)
res <- .Fortran(F_wu, as.double(gt), as.double(tol_lam),
as.integer(maxiter), as.integer(nrow(gt)),
as.integer(ncol(gt)), as.double(K),
conv=integer(1), obj=double(1),
lambda=double(ncol(gt)))
list(lambda=res$lambda, convergence=list(convergence=res$conv),
obj = res$obj)
}
.CUE_lam <- function(gt, K=1)
{
q <- qr(gt)
n <- nrow(gt)
l0 <- -qr.coef(q, rep(1,n))
conv <- list(convergence=0)
list(lambda = l0, convergence = conv, obj =
mean(.rho(gt,l0,derive=0,type="CUE",k=K)))
}
.CUE_lamPos <- function(gt, K=1, control=list())
{
getpt <- function(gt,lam)
{
gl <- c(gt%*%lam)
pt <- 1 + gl
pt/sum(pt)
}
maxit <- ifelse("maxit" %in% names(control),
control$maxit, 50)
res <-.CUE_lam(gt, K)
n <- nrow(gt)
i <- 1
pt <- getpt(gt, res$lambda)
w <- pt<0
while (TRUE)
{
gt2 <- gt[!w,]
n1 <- nrow(gt2)
if (n1 == n)
break
res <- try(.CUE_lam(gt2), silent=TRUE)
if (i > maxit)
return(list(lambda=rep(0,ncol(gt)), obj=0, pt=rep(1/n,n),
convergence=list(convergence=1)))
if (any(class(res) == "try-error"))
return(list(lambda=rep(0,ncol(gt)), obj=0, pt=rep(1/n,n),
convergence=list(convergence=2)))
pt[!w] <- getpt(gt2, res$lambda)
pt[w] <- 0
if (all(pt>=0))
break
i <- i+1
w[!w] <- pt[!w]<0
}
n0 <- n-n1
res$obj <- res$obj*n1/n + n0/(2*n)
res
}
.CUE_lamPos2 <- function(gt, K=1, control=list())
{
gt <- as.matrix(gt)
n <- nrow(gt)
q <- ncol(gt)
maxit <- ifelse("maxit" %in% names(control),
control$maxit, 50)
res <- try(.Fortran(F_lamcuep, as.double(gt),
as.integer(n), as.integer(q), as.double(K),
as.integer(maxit),conv=integer(1),
lam=double(q),pt=double(n),
obj=double(1)
), silent=TRUE)
if (any(class(res) == "try-error"))
return(list(lambda=rep(0,q), obj=0, pt=rep(1/n,n),
convergence=list(convergence=3)))
list(lambda=res$lam, obj=res$obj, pt=res$pt,
convergence=list(convergence=res$conv))
}
getLamb <- function(gt, l0, type = c('EL', 'ET', 'CUE', "ETEL", "HD", "ETHD", "RCUE"),
tol_lam = 1e-7, maxiterlam = 100, tol_obj = 1e-7,
k = 1, method = c("nlminb", "optim", "iter", "Wu"),
control=list())
{
method <- match.arg(method)
type <- match.arg(type)
gt <- as.matrix(gt)
if (method == "Wu" & type != "EL")
stop("Wu (2005) method to compute Lambda is for EL only")
if (method == "Wu")
return(.Wu2(gt, tol_lam, maxiterlam, k))
if (type == "CUE")
return(.CUE_lam(gt, k))
if (type == "RCUE")
return(.CUE_lamPos2(gt, k, control))
if (method == "iter")
{
if ((type == "ETEL") | (type == "ETHD"))
type = "ET"
for (i in 1:maxiterlam)
{
r1 <- .rho(gt,l0,derive=1,type=type,k=k)
r2 <- .rho(gt,l0,derive=2,type=type,k=k)
F <- -colMeans(r1*gt)
J <- crossprod(r2*gt,gt)
if (sum(abs(F))<tol_obj)
{
conv <- list(convergence="Tolerance for the FOC reached")
break
}
P <- solve(J,F)
if (sum(abs(P))<tol_lam)
{
conv <- list(convergence="Tolerance on lambda reached")
break
}
l0 <- l0 + P
conv <- list(convergence="maxiterlam reached")
}
} else {
fct <- function(l,X,type,k)
{
r0 <- .rho(X,l,derive=0,type=type,k=k)
-mean(r0)
}
Dfct <- function(l,X,type,k)
{
r1 <- .rho(X,l,derive=1,type=type,k=k)
-colMeans(r1*X)
}
DDfct <- function(l,X,type,k)
{
r2 <- .rho(X,l,derive=2,type=type,k=k)
-t(X*r2)%*%X/nrow(X)
}
if ((type == "ETEL")|(type=="ETHD"))
type = "ET"
if (method=="optim")
{
if (type != "EL")
{
res <- optim(rep(0,ncol(gt)),fct,gr=Dfct,X=gt,type=type,
k=k,method="BFGS",control=control)
} else {
ci <- -rep(1,nrow(gt))
res <- constrOptim(rep(0,ncol(gt)),fct,Dfct,-gt,ci,
control=control,X=gt,type=type,k=k)
}
} else {
res <- nlminb(rep(0,ncol(gt)), fct, gradient = Dfct,
hessian = DDfct, X = gt, type=type, k=k,
control = control)
}
l0 <- res$par
if (method == "optim" | method == "constrOptim")
conv <- list(convergence = res$convergence, counts = res$counts,
message = res$message)
if(method == "nlminb")
conv <- list(convergence = res$convergence, counts =
res$evaluations, message = res$message)
}
return(list(lambda = l0, convergence = conv, obj =
mean(.rho(gt,l0,derive=0,type=type,k=k))-
.rho(1, 0, type = type, derive = 0, k = k)))
}
smoothG <- function (x, bw = bwAndrews, prewhite = 1, ar.method = "ols",
weights = weightsAndrews,
kernel = c("Bartlett", "Parzen", "Truncated", "Tukey-Hanning"),
approx = c("AR(1)", "ARMA(1,1)"),
tol = 1e-7)
{
kernel <- match.arg(kernel)
approx <- match.arg(approx)
n <- nrow(x)
if (is.function(weights))
{
class(x) <- "gmmFct"
w <- weights(x, bw = bw, kernel = kernel,
prewhite = prewhite, ar.method = ar.method, tol = tol,
verbose = FALSE, approx = approx)
} else {
w <- weights
}
if (is.numeric(w))
{
rt <- length(w)
if (rt >= 2)
{
w <- c(w[rt:2], w)
w <- w / sum(w)
w <- kernel(w[rt:length(w)])
} else {
w <- kernel(1)
}
} else {
if (class(w)[1] != "tskernel")
stop("Provided weights must be a numeric vector or an object of class 'tskernel'")
}
if (length(w$coef)>1)
x <- kernapply(x, w)
sx <- list("smoothx" = x, "kern_weights" = w, bw = bw)
return(sx)
}
gel <- function(g, x, tet0 = NULL, gradv = NULL, smooth = FALSE,
type = c("EL", "ET", "CUE", "ETEL", "HD", "ETHD","RCUE"),
kernel = c("Truncated", "Bartlett"), bw = bwAndrews,
approx = c("AR(1)", "ARMA(1,1)"), prewhite = 1, ar.method = "ols",
tol_weights = 1e-7, tol_lam = 1e-9, tol_obj = 1e-9,
tol_mom = 1e-9, maxiterlam = 100, constraint = FALSE,
optfct = c("optim", "optimize", "nlminb"),
optlam = c("nlminb", "optim", "iter", "Wu"), data,
Lambdacontrol = list(),
model = TRUE, X = FALSE, Y = FALSE, TypeGel = "baseGel", alpha = NULL,
eqConst = NULL, eqConstFullVcov = FALSE, onlyCoefficients=FALSE, ...)
{
type <- match.arg(type)
optfct <- match.arg(optfct)
optlam <- match.arg(optlam)
weights <- weightsAndrews
approx <- match.arg(approx)
kernel <- match.arg(kernel)
if (!is.null(eqConst))
TypeGel <- "constGel"
if(missing(data))
data<-NULL
all_args <- list(g = g, x = x, tet0 = tet0, gradv = gradv, smooth = smooth,
type = type, kernel = kernel, bw = bw, approx = approx,
prewhite = prewhite, ar.method = ar.method,
tol_weights = tol_weights, tol_lam = tol_lam,
tol_obj = tol_obj, tol_mom = tol_mom, maxiterlam = maxiterlam,
constraint = constraint, optfct = optfct, weights = weights,
optlam = optlam, model = model, X = X, Y = Y,
TypeGel = TypeGel, call = match.call(),
Lambdacontrol = Lambdacontrol, alpha = alpha, data = data,
eqConst = eqConst, eqConstFullVcov = eqConstFullVcov,
onlyCoefficients=onlyCoefficients)
class(all_args)<-TypeGel
Model_info<-getModel(all_args)
z <- momentEstim(Model_info, ...)
if (!onlyCoefficients)
class(z) <- "gel"
return(z)
}
evalGel <- function(g, x, tet0, gradv = NULL, smooth = FALSE,
type = c("EL", "ET", "CUE", "ETEL", "HD", "ETHD","RCUE"),
kernel = c("Truncated", "Bartlett"), bw = bwAndrews,
approx = c("AR(1)", "ARMA(1,1)"), prewhite = 1,
ar.method = "ols", tol_weights = 1e-7, tol_lam = 1e-9,
tol_obj = 1e-9, tol_mom = 1e-9, maxiterlam = 100,
optlam = c("nlminb", "optim", "iter", "Wu"), data,
Lambdacontrol = list(),
model = TRUE, X = FALSE, Y = FALSE, alpha = NULL, ...)
{
type <- match.arg(type)
optlam <- match.arg(optlam)
weights <- weightsAndrews
approx <- match.arg(approx)
kernel <- match.arg(kernel)
TypeGel <- "baseGel"
if(missing(data))
data<-NULL
all_args <- list(g = g, x = x, tet0 = tet0, gradv = gradv, smooth = smooth,
type = type, kernel = kernel, bw = bw, approx = approx,
prewhite = prewhite, ar.method = ar.method,
tol_weights = tol_weights, tol_lam = tol_lam,
tol_obj = tol_obj, tol_mom = tol_mom, maxiterlam = maxiterlam,
weights = weights, optlam = optlam, model = model, X = X,
Y = Y, call = match.call(), Lambdacontrol = Lambdacontrol,
alpha = alpha, data = data, optfct="optim")
class(all_args)<-TypeGel
Model_info<-getModel(all_args)
class(Model_info) <- "baseGel.eval"
z <- momentEstim(Model_info, ...)
class(z) <- "gel"
return(z)
}
.thetf <- function(tet, P, output=c("obj","all"), l0Env)
{
output <- match.arg(output)
gt <- P$g(tet, P$x)
l0 <- get("l0",envir=l0Env)
if (((P$type=="ETEL")|(P$type=="ETHD"))&(!is.null(P$CGEL)))
{
P$CGEL <- NULL
warning("CGEL not implemented for ETEL or for ETHD")
}
if (is.null(P$CGEL))
{
if (P$optlam != "optim" & P$type == "EL")
{
lamb <- try(getLamb(gt, l0, type = P$type, tol_lam = P$tol_lam,
maxiterlam = P$maxiterlam,
tol_obj = P$tol_obj, k = P$k1/P$k2,
control = P$Lambdacontrol,
method = P$optlam), silent = TRUE)
if(any(class(lamb) == "try-error"))
lamb <- getLamb(gt, l0, type = P$type, tol_lam = P$tol_lam,
maxiterlam = P$maxiterlam,
tol_obj = P$tol_obj, k = P$k1/P$k2,
control = P$Lambdacontrol, method = "optim")
} else {
lamb <- getLamb(gt, l0, type = P$type, tol_lam = P$tol_lam,
maxiterlam = P$maxiterlam, tol_obj = P$tol_obj,
k = P$k1/P$k2, control = P$Lambdacontrol,
method = P$optlam)
}
} else {
lamb <- try(.getCgelLam(gt, l0, type = P$type, method = "nlminb",
control=P$Lambdacontrol, k = P$k1/P$k2,
alpha = P$CGEL),silent=TRUE)
if (any(class(lamb) == "try-error"))
lamb <- try(.getCgelLam(gt, l0, type = P$type,
method = "constrOptim",
control=P$Lambdacontrol,
k = P$k1/P$k2, alpha = P$CGEL),silent=TRUE)
}
if (P$type == "ETEL")
obj <- mean(.rho(gt, lamb$lambda, type = P$type, derive = 0,
k = P$k1/P$k2) - .rho(1, 0, type = P$type,
derive = 0, k = P$k1/P$k2))
else if (P$type == "ETHD")
obj <- sum(.rho(gt, lamb$lambda, type = P$type, derive = 0,
k = P$k1/P$k2) - .rho(1, 0, type = P$type, derive = 0,
k = P$k1/P$k2))
else
obj <- lamb$obj
assign("l0",lamb$lambda,envir=l0Env)
if(output == "obj")
return(obj)
else
return(list(obj = obj, lambda = lamb, gt = gt))
}
.getImpProb <- function(gt, lambda, type, k1, k2)
{
if ((type == "ETEL")|(type=="ETHD"))
type <- "ET"
n <- NROW(gt)
pt <- -.rho(gt, lambda, type = type, derive = 1, k = k1/k2)/n
# Making sure pt>0
if (type=="CUE")
{
eps <- -length(pt)*min(min(pt),0)
pt <- (pt+eps/length(pt))/(1+eps)
}
if (type=="RCUE")
pt[pt<0] <- 0
###################
conv_moment <- colSums(pt*gt)
conv_pt <- sum(as.numeric(pt))
pt <- pt/sum(pt)
attr(pt, "conv_moment") <- conv_moment
attr(pt, "conv_pt") <- conv_pt
pt
}
.vcovGel <- function(gt, G, k1, k2, bw, pt=NULL,tol=1e-16)
{
q <- NCOL(gt)
n <- NROW(gt)
if (is.null(pt))
pt <- 1/n
G <- G/k1
gt <- gt*sqrt(pt*bw/k2)
qrGt <- qr(gt)
piv <- sort.int(qrGt$pivot, index.return=TRUE)$ix
R <- qr.R(qrGt)[,piv]
X <- forwardsolve(t(R), G)
Y <- forwardsolve(t(R), diag(q))
res <- lm.fit(X,Y)
u <- res$residuals
Sigma <- chol2inv(res$qr$qr)/n
diag(Sigma)[diag(Sigma)<0] <- tol
if (q==ncol(G))
{
SigmaLam <- matrix(0, q, q)
} else {
SigmaLam <- backsolve(R, u)/n*bw^2
diag(SigmaLam)[diag(SigmaLam)<0] <- tol
}
khat <- crossprod(R)
list(vcov_par=Sigma, vcov_lambda=SigmaLam,khat=khat)
}
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Defines functions .vcovGel .getImpProb .thetf evalGel gel getLamb .CUE_lamPos2 .CUE_lamPos .CUE_lam .Wu2 .Wu .getCgelLam .rho
Documented in evalGel gel getLamb
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# A copy of the GNU General Public License is available at
# http://www.r-project.org/Licenses/
.rho <- function(x, lamb, derive = 0, type = c("EL", "ET", "CUE", "HD", "ETEL", "ETHD",
"RCUE"), k = 1)
{
type <- match.arg(type)
if (type == "RCUE")
type <- "CUE"
gml <- x%*%c(lamb)*k
if (derive == 0)
{
if (type == "EL")
{
if (any(gml>=1))
stop("Computation of Lambda fails because NAs produced by log(1-gt*l)")
rhomat <- log(1 - gml)
}
if (type == "ET")
rhomat <- -exp(gml)
if (type == "CUE")
rhomat <- -gml -0.5*gml^2
if (type == "HD")
rhomat <- -2/(1-gml/2)
if (type == "ETEL")
{
w <- -exp(gml)
w <- w/sum(w)
rhomat <- -log(w*NROW(gml))
}
if (type == "ETHD")
{
w <- -exp(gml)
w <- w/sum(w)
rhomat <- (sqrt(w)-1/sqrt(NROW(gml)))^2
}
}
if (derive==1)
{
if (type == "EL")
rhomat <- -1/(1 - gml)
if (type == "ET")
rhomat <- -exp(gml)
if (type == "CUE")
rhomat <- -1 - gml
if (type == "HD")
rhomat <- -1/((1-gml/2)^2)
if (any(type == c("ETEL","ETHD")))
rhomat <- NULL
}
if (derive==2)
{
if (type == "EL")
rhomat <- -1/(1 - gml)^2
if (type == "ET")
rhomat <- -exp(gml)
if (type == "CUE")
rhomat <- -rep(1,nrow(x))
if (type == "HD")
rhomat <- -1/((1-gml/2)^3)
if (any(type == c("ETEL","ETHD")))
rhomat <- NULL
}
return(c(rhomat))
}
.getCgelLam <- function(gt, l0, type = c('EL', 'ET', 'CUE', "HD"),
method = c("nlminb", "optim", "constrOptim"),
control=list(), k = 1, alpha = 0.01)
{
type <- match.arg(type)
method <- match.arg(method)
fct <- function(l, X)
{
r1 <- colMeans(.rho(gt,l,derive=1,type=type,k=k)*X)
crossprod(r1) + alpha*crossprod(l)
}
Dfct <- function(l, X)
{
r2 <- .rho(X,l,derive=2,type=type,k=k)
r1 <- .rho(X,l,derive=1,type=type,k=k)
H <- t(X*r2)%*%X/nrow(X)
2*H%*%colMeans(r1*X) + 2*alpha*l
}
if (method == "nlminb")
res <- nlminb(l0, fct, Dfct, X = gt, control = control)
if (method == "optim")
res <- optim(l0, fct, Dfct, X = gt, method="BFGS", control = control)
if (method == "constrOptim")
{
ci <- -rep(1,nrow(gt))
res <- constrOptim(rep(0,ncol(gt)),fct,Dfct,-gt,ci,control=control,X=gt)
}
if (method == "optim")
{
conv <- list(convergence = res$convergence,
counts = res$counts, message = res$message)
} else {
conv <- list(convergence = res$convergence, counts = res$evaluations,
message = res$message)
}
return(list(lambda = res$par, convergence = conv,
obj = mean(.rho(gt,res$par, derive=0,type=type,k=k)) -
.rho(1,0, derive=0,type=type,k=k)))
}
.Wu <- function(gt, tol_lam = 1e-8, maxiterlam = 50, K=1)
{
u <- as.matrix(gt)
n=length(nrow(u))
M=rep(0,ncol(u))
dif=1
tol=tol_lam
k=0
while(dif>tol & k<=maxiterlam)
{
D1=t(u)%*%((1/(1+u%*%M))*rep(1,n))
DD=-t(u)%*%(c((1/(1+u%*%M)^2))*u)
D2=solve(DD,D1,tol=1e-40)
dif=max(abs(D2))
rule=1
while(rule>0)
{
rule=0
if(min(1+t(M-D2)%*%t(u))<=0) rule=rule+1
if(rule>0) D2=D2/2
}
M=M-D2
k=k+1
}
if(k>=maxiterlam)
{
M=rep(0,ncol(u))
conv = list(convergence=1)
} else {
conv = list(convergence=0)
}
return(list(lambda = c(-M), convergence = conv, obj =
mean(.rho(gt,-M,derive=0,type="EL",k=K))))
}
.Wu2 <- function(gt, tol_lam = 1e-8, maxiter = 50, K = 1)
{
gt <- as.matrix(gt)
res <- .Fortran(F_wu, as.double(gt), as.double(tol_lam),
as.integer(maxiter), as.integer(nrow(gt)),
as.integer(ncol(gt)), as.double(K),
conv=integer(1), obj=double(1),
lambda=double(ncol(gt)))
list(lambda=res$lambda, convergence=list(convergence=res$conv),
obj = res$obj)
}
.CUE_lam <- function(gt, K=1)
{
q <- qr(gt)
n <- nrow(gt)
l0 <- -qr.coef(q, rep(1,n))
conv <- list(convergence=0)
list(lambda = l0, convergence = conv, obj =
mean(.rho(gt,l0,derive=0,type="CUE",k=K)))
}
.CUE_lamPos <- function(gt, K=1, control=list())
{
getpt <- function(gt,lam)
{
gl <- c(gt%*%lam)
pt <- 1 + gl
pt/sum(pt)
}
maxit <- ifelse("maxit" %in% names(control),
control$maxit, 50)
res <-.CUE_lam(gt, K)
n <- nrow(gt)
i <- 1
pt <- getpt(gt, res$lambda)
w <- pt<0
while (TRUE)
{
gt2 <- gt[!w,]
n1 <- nrow(gt2)
if (n1 == n)
break
res <- try(.CUE_lam(gt2), silent=TRUE)
if (i > maxit)
return(list(lambda=rep(0,ncol(gt)), obj=0, pt=rep(1/n,n),
convergence=list(convergence=1)))
if (any(class(res) == "try-error"))
return(list(lambda=rep(0,ncol(gt)), obj=0, pt=rep(1/n,n),
convergence=list(convergence=2)))
pt[!w] <- getpt(gt2, res$lambda)
pt[w] <- 0
if (all(pt>=0))
break
i <- i+1
w[!w] <- pt[!w]<0
}
n0 <- n-n1
res$obj <- res$obj*n1/n + n0/(2*n)
res
}
.CUE_lamPos2 <- function(gt, K=1, control=list())
{
gt <- as.matrix(gt)
n <- nrow(gt)
q <- ncol(gt)
maxit <- ifelse("maxit" %in% names(control),
control$maxit, 50)
res <- try(.Fortran(F_lamcuep, as.double(gt),
as.integer(n), as.integer(q), as.double(K),
as.integer(maxit),conv=integer(1),
lam=double(q),pt=double(n),
obj=double(1)
), silent=TRUE)
if (any(class(res) == "try-error"))
return(list(lambda=rep(0,q), obj=0, pt=rep(1/n,n),
convergence=list(convergence=3)))
list(lambda=res$lam, obj=res$obj, pt=res$pt,
convergence=list(convergence=res$conv))
}
getLamb <- function(gt, l0, type = c('EL', 'ET', 'CUE', "ETEL", "HD", "ETHD", "RCUE"),
tol_lam = 1e-7, maxiterlam = 100, tol_obj = 1e-7,
k = 1, method = c("nlminb", "optim", "iter", "Wu"),
control=list())
{
method <- match.arg(method)
type <- match.arg(type)
gt <- as.matrix(gt)
if (method == "Wu" & type != "EL")
stop("Wu (2005) method to compute Lambda is for EL only")
if (method == "Wu")
return(.Wu2(gt, tol_lam, maxiterlam, k))
if (type == "CUE")
return(.CUE_lam(gt, k))
if (type == "RCUE")
return(.CUE_lamPos2(gt, k, control))
if (method == "iter")
{
if ((type == "ETEL") | (type == "ETHD"))
type = "ET"
for (i in 1:maxiterlam)
{
r1 <- .rho(gt,l0,derive=1,type=type,k=k)
r2 <- .rho(gt,l0,derive=2,type=type,k=k)
F <- -colMeans(r1*gt)
J <- crossprod(r2*gt,gt)
if (sum(abs(F))<tol_obj)
{
conv <- list(convergence="Tolerance for the FOC reached")
break
}
P <- solve(J,F)
if (sum(abs(P))<tol_lam)
{
conv <- list(convergence="Tolerance on lambda reached")
break
}
l0 <- l0 + P
conv <- list(convergence="maxiterlam reached")
}
} else {
fct <- function(l,X,type,k)
{
r0 <- .rho(X,l,derive=0,type=type,k=k)
-mean(r0)
}
Dfct <- function(l,X,type,k)
{
r1 <- .rho(X,l,derive=1,type=type,k=k)
-colMeans(r1*X)
}
DDfct <- function(l,X,type,k)
{
r2 <- .rho(X,l,derive=2,type=type,k=k)
-t(X*r2)%*%X/nrow(X)
}
if ((type == "ETEL")|(type=="ETHD"))
type = "ET"
if (method=="optim")
{
if (type != "EL")
{
res <- optim(rep(0,ncol(gt)),fct,gr=Dfct,X=gt,type=type,
k=k,method="BFGS",control=control)
} else {
ci <- -rep(1,nrow(gt))
res <- constrOptim(rep(0,ncol(gt)),fct,Dfct,-gt,ci,
control=control,X=gt,type=type,k=k)
}
} else {
res <- nlminb(rep(0,ncol(gt)), fct, gradient = Dfct,
hessian = DDfct, X = gt, type=type, k=k,
control = control)
}
l0 <- res$par
if (method == "optim" | method == "constrOptim")
conv <- list(convergence = res$convergence, counts = res$counts,
message = res$message)
if(method == "nlminb")
conv <- list(convergence = res$convergence, counts =
res$evaluations, message = res$message)
}
return(list(lambda = l0, convergence = conv, obj =
mean(.rho(gt,l0,derive=0,type=type,k=k))-
.rho(1, 0, type = type, derive = 0, k = k)))
}
smoothG <- function (x, bw = bwAndrews, prewhite = 1, ar.method = "ols",
weights = weightsAndrews,
kernel = c("Bartlett", "Parzen", "Truncated", "Tukey-Hanning"),
approx = c("AR(1)", "ARMA(1,1)"),
tol = 1e-7)
{
kernel <- match.arg(kernel)
approx <- match.arg(approx)
n <- nrow(x)
if (is.function(weights))
{
class(x) <- "gmmFct"
w <- weights(x, bw = bw, kernel = kernel,
prewhite = prewhite, ar.method = ar.method, tol = tol,
verbose = FALSE, approx = approx)
} else {
w <- weights
}
if (is.numeric(w))
{
rt <- length(w)
if (rt >= 2)
{
w <- c(w[rt:2], w)
w <- w / sum(w)
w <- kernel(w[rt:length(w)])
} else {
w <- kernel(1)
}
} else {
if (class(w)[1] != "tskernel")
stop("Provided weights must be a numeric vector or an object of class 'tskernel'")
}
if (length(w$coef)>1)
x <- kernapply(x, w)
sx <- list("smoothx" = x, "kern_weights" = w, bw = bw)
return(sx)
}
gel <- function(g, x, tet0 = NULL, gradv = NULL, smooth = FALSE,
type = c("EL", "ET", "CUE", "ETEL", "HD", "ETHD","RCUE"),
kernel = c("Truncated", "Bartlett"), bw = bwAndrews,
approx = c("AR(1)", "ARMA(1,1)"), prewhite = 1, ar.method = "ols",
tol_weights = 1e-7, tol_lam = 1e-9, tol_obj = 1e-9,
tol_mom = 1e-9, maxiterlam = 100, constraint = FALSE,
optfct = c("optim", "optimize", "nlminb"),
optlam = c("nlminb", "optim", "iter", "Wu"), data,
Lambdacontrol = list(),
model = TRUE, X = FALSE, Y = FALSE, TypeGel = "baseGel", alpha = NULL,
eqConst = NULL, eqConstFullVcov = FALSE, onlyCoefficients=FALSE, ...)
{
type <- match.arg(type)
optfct <- match.arg(optfct)
optlam <- match.arg(optlam)
weights <- weightsAndrews
approx <- match.arg(approx)
kernel <- match.arg(kernel)
if (!is.null(eqConst))
TypeGel <- "constGel"
if(missing(data))
data<-NULL
all_args <- list(g = g, x = x, tet0 = tet0, gradv = gradv, smooth = smooth,
type = type, kernel = kernel, bw = bw, approx = approx,
prewhite = prewhite, ar.method = ar.method,
tol_weights = tol_weights, tol_lam = tol_lam,
tol_obj = tol_obj, tol_mom = tol_mom, maxiterlam = maxiterlam,
constraint = constraint, optfct = optfct, weights = weights,
optlam = optlam, model = model, X = X, Y = Y,
TypeGel = TypeGel, call = match.call(),
Lambdacontrol = Lambdacontrol, alpha = alpha, data = data,
eqConst = eqConst, eqConstFullVcov = eqConstFullVcov,
onlyCoefficients=onlyCoefficients)
class(all_args)<-TypeGel
Model_info<-getModel(all_args)
z <- momentEstim(Model_info, ...)
if (!onlyCoefficients)
class(z) <- "gel"
return(z)
}
evalGel <- function(g, x, tet0, gradv = NULL, smooth = FALSE,
type = c("EL", "ET", "CUE", "ETEL", "HD", "ETHD","RCUE"),
kernel = c("Truncated", "Bartlett"), bw = bwAndrews,
approx = c("AR(1)", "ARMA(1,1)"), prewhite = 1,
ar.method = "ols", tol_weights = 1e-7, tol_lam = 1e-9,
tol_obj = 1e-9, tol_mom = 1e-9, maxiterlam = 100,
optlam = c("nlminb", "optim", "iter", "Wu"), data,
Lambdacontrol = list(),
model = TRUE, X = FALSE, Y = FALSE, alpha = NULL, ...)
{
type <- match.arg(type)
optlam <- match.arg(optlam)
weights <- weightsAndrews
approx <- match.arg(approx)
kernel <- match.arg(kernel)
TypeGel <- "baseGel"
if(missing(data))
data<-NULL
all_args <- list(g = g, x = x, tet0 = tet0, gradv = gradv, smooth = smooth,
type = type, kernel = kernel, bw = bw, approx = approx,
prewhite = prewhite, ar.method = ar.method,
tol_weights = tol_weights, tol_lam = tol_lam,
tol_obj = tol_obj, tol_mom = tol_mom, maxiterlam = maxiterlam,
weights = weights, optlam = optlam, model = model, X = X,
Y = Y, call = match.call(), Lambdacontrol = Lambdacontrol,
alpha = alpha, data = data, optfct="optim")
class(all_args)<-TypeGel
Model_info<-getModel(all_args)
class(Model_info) <- "baseGel.eval"
z <- momentEstim(Model_info, ...)
class(z) <- "gel"
return(z)
}
.thetf <- function(tet, P, output=c("obj","all"), l0Env)
{
output <- match.arg(output)
gt <- P$g(tet, P$x)
l0 <- get("l0",envir=l0Env)
if (((P$type=="ETEL")|(P$type=="ETHD"))&(!is.null(P$CGEL)))
{
P$CGEL <- NULL
warning("CGEL not implemented for ETEL or for ETHD")
}
if (is.null(P$CGEL))
{
if (P$optlam != "optim" & P$type == "EL")
{
lamb <- try(getLamb(gt, l0, type = P$type, tol_lam = P$tol_lam,
maxiterlam = P$maxiterlam,
tol_obj = P$tol_obj, k = P$k1/P$k2,
control = P$Lambdacontrol,
method = P$optlam), silent = TRUE)
if(any(class(lamb) == "try-error"))
lamb <- getLamb(gt, l0, type = P$type, tol_lam = P$tol_lam,
maxiterlam = P$maxiterlam,
tol_obj = P$tol_obj, k = P$k1/P$k2,
control = P$Lambdacontrol, method = "optim")
} else {
lamb <- getLamb(gt, l0, type = P$type, tol_lam = P$tol_lam,
maxiterlam = P$maxiterlam, tol_obj = P$tol_obj,
k = P$k1/P$k2, control = P$Lambdacontrol,
method = P$optlam)
}
} else {
lamb <- try(.getCgelLam(gt, l0, type = P$type, method = "nlminb",
control=P$Lambdacontrol, k = P$k1/P$k2,
alpha = P$CGEL),silent=TRUE)
if (any(class(lamb) == "try-error"))
lamb <- try(.getCgelLam(gt, l0, type = P$type,
method = "constrOptim",
control=P$Lambdacontrol,
k = P$k1/P$k2, alpha = P$CGEL),silent=TRUE)
}
if (P$type == "ETEL")
obj <- mean(.rho(gt, lamb$lambda, type = P$type, derive = 0,
k = P$k1/P$k2) - .rho(1, 0, type = P$type,
derive = 0, k = P$k1/P$k2))
else if (P$type == "ETHD")
obj <- sum(.rho(gt, lamb$lambda, type = P$type, derive = 0,
k = P$k1/P$k2) - .rho(1, 0, type = P$type, derive = 0,
k = P$k1/P$k2))
else
obj <- lamb$obj
assign("l0",lamb$lambda,envir=l0Env)
if(output == "obj")
return(obj)
else
return(list(obj = obj, lambda = lamb, gt = gt))
}
.getImpProb <- function(gt, lambda, type, k1, k2)
{
if ((type == "ETEL")|(type=="ETHD"))
type <- "ET"
n <- NROW(gt)
pt <- -.rho(gt, lambda, type = type, derive = 1, k = k1/k2)/n
# Making sure pt>0
if (type=="CUE")
{
eps <- -length(pt)*min(min(pt),0)
pt <- (pt+eps/length(pt))/(1+eps)
}
if (type=="RCUE")
pt[pt<0] <- 0
###################
conv_moment <- colSums(pt*gt)
conv_pt <- sum(as.numeric(pt))
pt <- pt/sum(pt)
attr(pt, "conv_moment") <- conv_moment
attr(pt, "conv_pt") <- conv_pt
pt
}
.vcovGel <- function(gt, G, k1, k2, bw, pt=NULL,tol=1e-16)
{
q <- NCOL(gt)
n <- NROW(gt)
if (is.null(pt))
pt <- 1/n
G <- G/k1
gt <- gt*sqrt(pt*bw/k2)
qrGt <- qr(gt)
piv <- sort.int(qrGt$pivot, index.return=TRUE)$ix
R <- qr.R(qrGt)[,piv]
X <- forwardsolve(t(R), G)
Y <- forwardsolve(t(R), diag(q))
res <- lm.fit(X,Y)
u <- res$residuals
Sigma <- chol2inv(res$qr$qr)/n
diag(Sigma)[diag(Sigma)<0] <- tol
if (q==ncol(G))
{
SigmaLam <- matrix(0, q, q)
} else {
SigmaLam <- backsolve(R, u)/n*bw^2
diag(SigmaLam)[diag(SigmaLam)<0] <- tol
}
khat <- crossprod(R)
list(vcov_par=Sigma, vcov_lambda=SigmaLam,khat=khat)
}
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