R/3_distances_disc.R In anjaweigel/mixComp_package: Estimation of the Order of Finite Mixture Distributions

Documented in hellinger.boot.dischellinger.discL2.boot.discL2.disc

```## Purpose: returns the L2 distance function corresponding to parameters x

.get.fmin.L2 <- function(dat, dist, formals.dist, ndistparams, j, n.inf, N, dist_call){

function(x){

w <- x[1:(j - 1)]

# first term of difference: sum over values up to "n.inf"
theta.list.long <- vector(mode = "list", length = ndistparams)
names(theta.list.long) <- formals.dist
for(i in 1:ndistparams){
theta.list.long[[i]] <- matrix(x[(i*j):((1 + i)*j - 1)], nrow = (n.inf + 1), ncol = j,
byrow = TRUE)
}
theta.list.long\$x <- 0:n.inf

# # NAs or warnings can happen as solnp sometimes uses intermediate
# # parameter values outside of the box constraints (to speed up convergence
# # and avoid numerical ill conditioning)
mat <- suppressWarnings(do.call(dist_call, args = theta.list.long))
w <- c(x[1:(j - 1)], 1 - sum(x[1:(j - 1)]))
if(any(w < 0)) return(sqrt(.Machine\$integer.max))
f.theta <- as.matrix(mat) %*% w
if(any(is.na(f.theta))) return(sqrt(.Machine\$integer.max))
f.theta.sq <- f.theta^2
f.1 <- sum(f.theta.sq) # first term of difference

# second term of difference: sum over the data as we multiply with the empirical
#                            distribution function
for(i in 1:ndistparams){
theta.list.long[[i]] <- matrix(x[(i*j):((1 + i)*j - 1)], nrow = N, ncol = j,
byrow = TRUE)
}
theta.list.long\$x <- dat

# # NAs or warnings can happen as solnp sometimes uses intermediate
# # parameter values outside of the box constraints (to speed up convergence
# # and avoid numerical ill conditioning)
mat <- suppressWarnings(do.call(dist_call, args = theta.list.long))
w <- c(x[1:(j - 1)], 1 - sum(x[1:(j - 1)]))
if(any(w < 0)) return(sqrt(.Machine\$integer.max))
f.theta.obs <- as.matrix(mat) %*% w
if(any(is.na(f.theta.obs))) return(sqrt(.Machine\$integer.max))
f.2 <- (2/N)*sum(f.theta.obs) # second term of difference

return(f.1 - f.2)
}
}

## Purpose: returns the L2 distance function corresponding to parameters x
##          when the mixture consists of only a single component

.get.fmin.L2.0 <- function(dat, dist, formals.dist, ndistparams, n.inf, N,  dist_call){

function(x){

# first term of difference: sum over values up to "n.inf"
theta.list.long <- vector(mode = "list", length = ndistparams)
names(theta.list.long) <- formals.dist
for(i in 1:ndistparams){
theta.list.long[[i]] <- rep(x[i], n.inf + 1)
}
theta.list.long\$x <- 0:n.inf

# # NAs or warnings can happen as solnp sometimes uses intermediate
# # parameter values outside of the box constraints (to speed up convergence
# # and avoid numerical ill conditioning)
f.theta <- suppressWarnings(do.call(dist_call, args = theta.list.long))
if(any(is.na(f.theta))) return(sqrt(.Machine\$integer.max))
f.theta.sq <- f.theta^2
f.1 <- sum(f.theta.sq)

# second term of difference: sum over the data as we multiply with the empirical
#                            distribution function
for(i in 1:ndistparams){
theta.list.long[[i]] <- rep(x[i], N)
}
theta.list.long\$x <- dat

# NAs or warnings can happen as solnp sometimes uses intermediate
# parameter values outside of the box constraints (to speed up convergence
# and avoid numerical ill conditioning)
f.components.obs <- suppressWarnings(do.call(dist_call, args = theta.list.long))
if (any(is.na(f.components.obs))) return(sqrt(.Machine\$integer.max))
f.theta.obs <- sum(f.components.obs)
f.2 <- (2/N)*sum(f.theta.obs)

return(f.1 - f.2)
}
}

## Purpose: L2 distance based method of estimating the mixture complexity of a
##          discrete mixture (as well as the weights and component parameters) returning
##          a 'paramEst' object

L2.disc <- function(obj, j.max = 10, n.inf = 1000, threshold = "SBC", control = c(trace = 0)){

# get standard variables
variable_list <- .get.list(obj)
list2env(variable_list, envir = environment())

# check relevant inputs
.input.checks.functions(obj, thrshL2 = threshold, j.max = j.max, n.inf = n.inf,
discrete = discrete, Hankel = FALSE, param = TRUE)
j0 <- 0

repeat{

j0 <- j0 + 1 # current complexity estimate
j1 <- j0 + 1

if(is.function(threshold)){
thresh <- threshold(n = N, j = j0)
}
else if(threshold == "LIC"){
thresh <- (0.6*log((j1)/j0))/N
}
else if (threshold == "SBC"){
thresh <- (0.6*log(N)*log((j1)/j0))/N
}

if(j0 > 1){ # if j1 was calculated in the last interation, pass it over to j0...

theta.j0 <- theta.j1
L2.j0 <- L2.j1
conv.j0 <- conv.j1
values.j0 <- values.j1

} else { # ... or calculate j0 directly if j0 = 1 (j1 has not been calculated yet)
# in this case we already know w = 1 (single component mixture)

fmin <- .get.fmin.L2.0(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, n.inf = n.inf, N = N, dist_call)

restrictions <- .get.restrictions(j = j0, ndistparams = ndistparams, lower = lower,
upper = upper)
lx <- restrictions\$lx
ux <- restrictions\$ux
initial.j0 <- .get.initialvals(dat, j0, ndistparams, MLE.function, lower, upper, dist,
formals.dist)

opt <- solnp(initial.j0, fun = fmin, LB = lx, UB = ux, control = control)
.printresults(opt, j0, dist, formals.dist, ndistparams)
theta.j0 <- opt\$pars
L2.j0 <- opt\$values[length(opt\$values)]
conv.j0 <- opt\$convergence
values.j0 <- opt\$values
}

# optimization for j1. Starts from j1 = 2 so we always need to include weight
# restrictions in optimization

fmin <- .get.fmin.L2(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, j = j1, n.inf = n.inf, N = N, dist_call)

restrictions.j1 <- .get.restrictions(j = j1, ndistparams = ndistparams, lower = lower,
upper = upper)
ineq <- restrictions\$ineq
lx.j1 <- restrictions.j1\$lx
ux.j1 <- restrictions.j1\$ux
initial.j1 <- .get.initialvals(dat, j1, ndistparams, MLE.function, lower, upper, dist,
formals.dist)

opt <- solnp(initial.j1, fun = fmin, LB = lx.j1, UB = ux.j1, ineqfun = ineq,
ineqLB = 0, ineqUB = 1, control = control)
theta.j1 <- opt\$pars <- .augment.pars(opt\$pars, j1)
L2.j1 <- opt\$values[length(opt\$values)] <- fmin(opt\$pars)
conv.j1 <- opt\$convergence
values.j1 <- opt\$values

.printresults(opt, j1, dist, formals.dist, ndistparams)

if((L2.j0 - L2.j1) < thresh){
break
} else if(j0 == j.max){
break
}

}

.return.paramEst(j0, j.max, dat, theta.j0, values.j0, conv.j0, dist, ndistparams, formals.dist,
discrete, MLE.function = NULL)
}

## Purpose: L2 distance based method of estimating the mixture complexity of a
##          discrete mixture (as well as the weights and component parameters) returning
##          a 'paramEst' object (using bootstrap)

L2.boot.disc <- function(obj, j.max = 10, n.inf = 1000, B = 100, ql = 0.025, qu = 0.975,
control = c(trace = 0), ...){

# get standard variables
variable_list <- .get.list(obj)
list2env(variable_list, envir = environment())

# check relevant inputs
.input.checks.functions(obj, j.max = j.max, B = B, n.inf = n.inf, ql = ql, qu = qu,
discrete = discrete, Hankel = FALSE, param = TRUE)
j0 <- 0

repeat{

j0 <- j0 + 1 # current complexity estimate
j1 <- j0 + 1

if(j0 > 1){ # if j1 was calculated in the last interation, pass it over to j0...

theta.j0 <- theta.j1
L2.j0 <- L2.j1
conv.j0 <- conv.j1
values.j0 <- values.j1

# also need to pass over the restrictions as they will be used in the bootstrap
ineq.j0 <- ineq.j1
lx.j0 <- lx.j1
ux.j0 <- ux.j1

} else { # ... or calculate j0 directly if j0 = 1 (j1 has not been calculated yet)
# in this case we already know w = 1 (single component mixture)

fmin.j0 <- .get.fmin.L2.0(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, n.inf = n.inf, N = N, dist_call)

restrictions.j0 <- .get.restrictions(j = j0, ndistparams = ndistparams, lower = lower,
upper = upper)
lx.j0 <- restrictions.j0\$lx
ux.j0 <- restrictions.j0\$ux
initial.j0 <- .get.initialvals(dat, j0, ndistparams, MLE.function, lower, upper,
dist, formals.dist)

opt <- solnp(initial.j0, fun = fmin.j0, LB = lx.j0, UB = ux.j0, control = control)
.printresults(opt, j0, dist, formals.dist, ndistparams)
theta.j0 <- opt\$pars
L2.j0 <- opt\$values[length(opt\$values)]
conv.j0 <- opt\$convergence
values.j0 <- opt\$values
}

# optimization for j1. Starts from j1 = 2 so we always need to include weight
# restrictions in optimization

fmin.j1 <- .get.fmin.L2(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, j = j1, n.inf = n.inf, N = N, dist_call)

restrictions.j1 <- .get.restrictions(j = j1, ndistparams = ndistparams, lower = lower,
upper = upper)
ineq.j1 <- restrictions.j1\$ineq
lx.j1 <- restrictions.j1\$lx
ux.j1 <- restrictions.j1\$ux
initial.j1 <- .get.initialvals(dat, j1, ndistparams, MLE.function, lower, upper,
dist, formals.dist)

opt <- solnp(initial.j1, fun = fmin.j1, ineqfun = ineq.j1, ineqLB = 0, ineqUB = 1,
LB = lx.j1, UB = ux.j1, control = control)
theta.j1 <- opt\$pars <- .augment.pars(opt\$pars, j1)
L2.j1 <- opt\$values[length(opt\$values)] <- fmin.j1(opt\$pars)
conv.j1 <- opt\$convergence
values.j1 <- opt\$values

.printresults(opt, j1, dist, formals.dist, ndistparams)

diff.0 <- L2.j0 - L2.j1

# parameters used for parametric bootstrap and corresponding 'Mix' object
param.list.boot <- .get.bootstrapparams(formals.dist = formals.dist, ndistparams = ndistparams,
mle.est = theta.j0, j = j0)
Mix.boot <- Mix(dist = dist, w = param.list.boot\$w, theta.list = param.list.boot\$theta.list,
name = "Mix.boot")

ran.gen <- function(dat, mle){
rMix(n = length(dat), obj = mle)
}

# counting bootstrap iterations to print progression
bs_iter <- -1

stat <- function(dat){

assign("bs_iter", bs_iter + 1, inherits = TRUE)
if(bs_iter != 0){

# don't include first iteration as this just uses the original data
# to calculate t0
cat(paste("Running bootstrap iteration ", bs_iter, " testing for ", j0,
" components.\n", sep = ""))

} else cat(paste("\n"))

# in the bootstrap we have to calculate the values for j0 and j1 as the bootstrap
# data changes in every iteration (cannot reuse last j1 values as j0)
initial.boot0 <- .get.initialvals(dat, j0, ndistparams, MLE.function, lower, upper,
dist, formals.dist)

# calculate optimal parameters for j0
if(j0 != 1){ # need to include weight restrictions in optimization

fmin.boot0 <- .get.fmin.L2(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, j = j0, n.inf = n.inf, N = N, dist_call)
opt.boot0 <- solnp(initial.boot0, fun = fmin.boot0, ineqfun = ineq.j0, ineqLB = 0,
ineqUB = 1, LB = lx.j0, UB = ux.j0, control = control)
opt.boot0\$pars <- .augment.pars(opt.boot0\$pars, j0)
L2.boot0 <- fmin.boot0(opt.boot0\$pars)

} else { # already know w = 1 (single component mixture)

fmin.boot0 <- .get.fmin.L2.0(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, n.inf = n.inf, N = N, dist_call)
opt.boot0 <- solnp(initial.boot0, fun = fmin.boot0, LB = lx.j0, UB = ux.j0,
control = control)
L2.boot0 <- opt.boot0\$values[length(opt.boot0\$values)]

}

# calculate optimal parameters for j1 (always need weight restrictions since j1
# starts from 2)
fmin.boot1 <- .get.fmin.L2(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, j = j1, n.inf = n.inf, N = N, dist_call)

initial.boot1 <- .get.initialvals(dat, j1, ndistparams, MLE.function, lower, upper,
dist, formals.dist)

opt.boot1 <- solnp(initial.boot1, fun = fmin.boot1, ineqfun = ineq.j1, ineqLB = 0,
ineqUB = 1, LB = lx.j1, UB = ux.j1, control = control)
opt.boot1\$pars <- .augment.pars(opt.boot1\$pars, j1)
L2.boot1 <- fmin.boot1(opt.boot1\$pars)

return(L2.boot0 - L2.boot1)
}

bt <- boot(dat, statistic = stat, R = B, sim = "parametric", ran.gen = ran.gen,
mle = Mix.boot, ...)
diff.boot <- bt\$t

q_lower <- quantile(diff.boot, probs = ql)
q_upper <- quantile(diff.boot, probs = qu)

if(diff.0 >= q_lower && diff.0 <= q_upper){
# so that the printed result reflects that the order j.max was actually estimated
# rather than just returned as the default
j.max <- j.max + 1
break
} else if (j0 == j.max){
break
}

}

.return.paramEst(j0, j.max, dat, theta.j0, values.j0, conv.j0, dist, ndistparams, formals.dist,
discrete, MLE.function = NULL)
}

## Purpose: returns the squareroot of the empirical mass function needed for hellinger
##          distance calculation

.get.f.n.sqrt <- function(dat, n.max, N){

# calculating square root of the empirical mass function
f.n <- as.numeric(table(dat)[match(0:n.max, sort(unique(dat)))]/N)
f.n[is.na(f.n)] <- 0
f.n.sqrt <- sqrt(f.n)

}

## Purpose: returns the Hellinger distance function corresponding to parameters x

.get.fmin.hellinger <- function(dat, dist, formals.dist, ndistparams, j, n.max, N,
f.n.sqrt, dist_call){

function(x){

w <- x[1:(j-1)]

# calculating square root of mixture distribution corresponding to the parameters x
theta.list.long <- vector(mode = "list", length = ndistparams)
names(theta.list.long) <- formals.dist
for(i in 1:ndistparams){
theta.list.long[[i]] <- matrix(x[(i*j):((1 + i)*j-1)], nrow = (n.max+1), ncol = j, byrow = TRUE)
}
theta.list.long\$x <- 0:n.max

# # NAs or warnings can happen as solnp sometimes uses intermediate
# # parameter values outside of the box constraints (to speed up convergence
# # and avoid numerical ill conditioning)
mat <- suppressWarnings(do.call(dist_call, args = theta.list.long))
w <- c(x[1:(j - 1)], 1 - sum(x[1:(j - 1)]))
if(any(w < 0)) return(sqrt(.Machine\$integer.max))
f.theta <- as.matrix(mat) %*% w
if(any(is.na(f.theta))) return(sqrt(.Machine\$integer.max))
f.theta.sqrt <- sqrt(f.theta)

# calculate Hellinger distance to empirical mass function
H2 <- f.n.sqrt * f.theta.sqrt
return(2 - 2 * sum(H2))
}
}

## Purpose: returns the Hellinger distance function corresponding to parameters x
##          when the mixture consists of only a single component

.get.fmin.hellinger.0 <- function(dat, dist, formals.dist, ndistparams, n.max, N,
f.n.sqrt, dist_call){

function(x){

# calculating square root of mixture distribution corresponding to the parameters x
# (single component mixture)
theta.list.long <- vector(mode = "list", length = ndistparams)
names(theta.list.long) <- formals.dist
for(i in 1:ndistparams){
theta.list.long[[i]] <- rep(x[i], n.max+1)
}
theta.list.long\$x <- 0:n.max

# # NAs or warnings can happen as solnp sometimes uses intermediate
# # parameter values outside of the box constraints (to speed up convergence
# # and avoid numerical ill conditioning)
f.components <- suppressWarnings(do.call(dist_call, args = theta.list.long))
if(any(is.na(f.components))) return(sqrt(.Machine\$integer.max))
f.components.sqrt <- sqrt(f.components)

# calculate Hellinger distance to empirical mass function
H2 <- f.n.sqrt*f.components.sqrt
return(2 - 2*sum(H2))
}
}

## Purpose: Hellinger distance based method of estimating the mixture complexity of a
##          discrete mixture (as well as the weights and component parameters) returning
##          a 'paramEst' object

hellinger.disc <- function(obj, j.max = 10, threshold = "SBC", control = c(trace = 0)){

# get standard variables
variable_list <- .get.list(obj)
list2env(variable_list, envir = environment())

# check relevant inputs
.input.checks.functions(obj, j.max = j.max, thrshHel = threshold,
discrete = discrete, Hankel = FALSE, param = TRUE)
j0 <- 0

if(is.character(threshold)){
# otherwise it is a function and will be calculated further down
if(threshold == "AIC") thresh <- (ndistparams + 1)/N
if(threshold == "SBC") thresh <- ((ndistparams + 1) * log(N))/(2 * N)
}

repeat{

j0 <- j0 + 1 # current complexity estimate
j1 <- j0 + 1

if(is.function(threshold)){
thresh <- threshold(n = N, j = j0)
}

f.n.sqrt <- .get.f.n.sqrt(dat, n.max, N)

if(j0 > 1){ # if j1 was calculated in the last interation, pass it over to j0...

theta.j0 <- theta.j1
Hellinger.j0 <- Hellinger.j1
conv.j0 <- conv.j1
values.j0 <- values.j1

} else { # ... or calculate j0 directly if j0 = 1 (j1 has not been calculated yet)
# in this case we already know w = 1 (single component mixture)

fmin <- .get.fmin.hellinger.0(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, n.max = n.max, N = N,
f.n.sqrt = f.n.sqrt, dist_call)

restrictions <- .get.restrictions(j = j0, ndistparams = ndistparams, lower = lower,
upper = upper)
lx <- restrictions\$lx
ux <- restrictions\$ux
initial.j0 <- .get.initialvals(dat, j0, ndistparams, MLE.function, lower, upper,
dist, formals.dist)

opt <- solnp(initial.j0, fun = fmin, LB = lx, UB = ux, control = control)
.printresults(opt, j0, dist, formals.dist, ndistparams)
theta.j0 <- opt\$pars
Hellinger.j0 <- opt\$values[length(opt\$values)]
conv.j0 <- opt\$convergence
values.j0 <- opt\$values
}

# optimization for j1. Starts from j1 = 2 so we always need to include weight
# restrictions in optimization

fmin <- .get.fmin.hellinger(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, j = j1, n.max = n.max, N = N,
f.n.sqrt = f.n.sqrt, dist_call)

restrictions.j1 <- .get.restrictions(j = j1, ndistparams = ndistparams, lower = lower,
upper = upper)
ineq.j1 <- restrictions.j1\$ineq
lx.j1 <- restrictions.j1\$lx
ux.j1 <- restrictions.j1\$ux
initial.j1 <- .get.initialvals(dat, j1, ndistparams, MLE.function, lower, upper, dist,
formals.dist)

opt <- solnp(initial.j1, fun = fmin, ineqfun = ineq.j1, ineqLB = 0, ineqUB = 1,
LB = lx.j1, UB = ux.j1, control = control)
theta.j1 <- opt\$pars <- .augment.pars(opt\$pars, j1)
Hellinger.j1 <- opt\$values[length(opt\$values)] <- fmin(opt\$pars)
conv.j1 <- opt\$convergence
values.j1 <- opt\$values

.printresults(opt, j1, dist, formals.dist, ndistparams)

if((Hellinger.j0 - Hellinger.j1) < thresh){
# so that the printed result reflects that the order j.max was actually estimated
# rather than just returned as the default
j.max <- j.max + 1
break
} else if(j0 == j.max){
break
}

}

.return.paramEst(j0, j.max, dat, theta.j0, values.j0, conv.j0, dist, ndistparams, formals.dist,
discrete, MLE.function)
}

## Purpose: Hellinger distance based method of estimating the mixture complexity of a
##          discrete mixture (as well as the weights and component parameters) returning
##          a 'paramEst' object (using bootstrap)

hellinger.boot.disc <- function(obj, j.max = 10, B = 100, ql = 0.025, qu = 0.975,
control = c(trace = 0), ...){

# get standard variables
variable_list <- .get.list(obj)
list2env(variable_list, envir = environment())

# check relevant inputs
.input.checks.functions(obj, j.max = j.max, B = B, ql = ql, qu = qu,
discrete = discrete, Hankel = FALSE, param = TRUE)
j0 <- 0

repeat{

j0 <- j0 + 1 # current complexity estimate
j1 <- j0 + 1

f.n.sqrt <- .get.f.n.sqrt(dat, n.max, N)

if(j0 > 1){ # if j1 was calculated in the last interation, pass it over to j0...

theta.j0 <- theta.j1
Hellinger.j0 <- Hellinger.j1
conv.j0 <- conv.j1
values.j0 <- values.j1

# also need to pass over the restrictions as they will be used in the bootstrap
ineq.j0 <- ineq.j1
lx.j0 <- lx.j1
ux.j0 <- ux.j1

} else { # ... or calculate j0 directly if j0 = 1 (j1 has not been calculated yet)
# in this case we already know w = 1 (single component mixture)

fmin.j0 <- .get.fmin.hellinger.0(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, n.max = n.max, N = N,
f.n.sqrt = f.n.sqrt, dist_call)

restrictions.j0 <- .get.restrictions(j = j0, ndistparams = ndistparams, lower = lower,
upper = upper)
lx.j0 <- restrictions.j0\$lx
ux.j0 <- restrictions.j0\$ux
initial.j0 <- .get.initialvals(dat, j0, ndistparams, MLE.function, lower, upper, dist,
formals.dist)

opt <- solnp(initial.j0, fun = fmin.j0, LB = lx.j0, UB = ux.j0, control = control)
.printresults(opt, j0, dist, formals.dist, ndistparams)
theta.j0 <- opt\$pars
Hellinger.j0 <- opt\$values[length(opt\$values)]
conv.j0 <- opt\$convergence
values.j0 <- opt\$values
}

# optimization for j1. Starts from j1 = 2 so we always need to include weight
# restrictions in optimization

fmin.j1 <- .get.fmin.hellinger(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, j = j1, n.max = n.max, N = N,
f.n.sqrt = f.n.sqrt, dist_call)

restrictions.j1 <- .get.restrictions(j = j1, ndistparams = ndistparams, lower = lower,
upper = upper)
ineq.j1 <- restrictions.j1\$ineq
lx.j1 <- restrictions.j1\$lx
ux.j1 <- restrictions.j1\$ux
initial.j1 <- .get.initialvals(dat, j1, ndistparams, MLE.function, lower, upper, dist,
formals.dist)

opt <- solnp(initial.j1, fun = fmin.j1, ineqfun = ineq.j1, ineqLB = 0, ineqUB = 1,
LB = lx.j1, UB = ux.j1, control = control)
theta.j1 <- opt\$pars <- .augment.pars(opt\$pars, j1)
Hellinger.j1 <- opt\$values[length(opt\$values)] <- fmin.j1(opt\$pars)
conv.j1 <- opt\$convergence
values.j1 <- opt\$values

.printresults(opt, j1, dist, formals.dist, ndistparams)

diff.0 <- Hellinger.j0 - Hellinger.j1

# parameters used for parametric bootstrap and corresponding 'Mix' object
param.list.boot <- .get.bootstrapparams(formals.dist = formals.dist, ndistparams = ndistparams,
mle.est = theta.j0, j = j0)
Mix.boot <- Mix(dist = dist, w = param.list.boot\$w, theta.list = param.list.boot\$theta.list,
name = "Mix.boot")

ran.gen <- function(dat, mle){
rMix(n = length(dat), obj = mle)
}

# counting bootstrap iterations to print progression
bs_iter <- -1

stat <- function(dat){

assign("bs_iter", bs_iter + 1, inherits = TRUE)
if(bs_iter != 0){

# don't include first iteration as this just uses the original data
# to calculate t0
cat(paste("Running bootstrap iteration ", bs_iter, " testing for ", j0,
" components.\n", sep = ""))

} else cat(paste("\n"))

f.n.sqrt.boot <- .get.f.n.sqrt(dat, n.max, N)

# in the bootstrap we have to calculate the values for j0 and j1 as the bootstrap
# data changes in every iteration (cannot reuse last j1 values as j0)

initial.boot0 <- .get.initialvals(dat, j0, ndistparams, MLE.function, lower, upper, dist,
formals.dist)

# calculate optimal parameters for j0
if(j0 != 1){ # need to include weight restrictions in optimization

fmin.boot0 <- .get.fmin.hellinger(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, j = j0, n.max = n.max, N = N,
f.n.sqrt = f.n.sqrt.boot, dist_call)
opt.boot0 <- solnp(initial.boot0, fun = fmin.boot0, ineqfun = ineq.j0, ineqLB = 0,
ineqUB = 1, LB = lx.j0, UB = ux.j0, control = control)
opt.boot0\$pars <- .augment.pars(opt.boot0\$pars, j0)
hellinger.boot0 <- fmin.boot0(opt.boot0\$pars)

} else { # already know w = 1 (single component mixture)

fmin.boot0 <- .get.fmin.hellinger.0(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, n.max = n.max, N = N,
f.n.sqrt = f.n.sqrt.boot, dist_call)
opt.boot0 <- solnp(initial.boot0, fun = fmin.boot0, LB = lx.j0, UB = ux.j0,
control = control)
hellinger.boot0 <- opt.boot0\$values[length(opt.boot0\$values)]

}

# calculate optimal parameters for j1 (always need weight restrictions since j1
# starts from 2)

fmin.boot1 <- .get.fmin.hellinger(dat = dat, dist = dist, formals.dist = formals.dist,
ndistparams = ndistparams, j = j1, n.max = n.max, N = N,
f.n.sqrt = f.n.sqrt.boot, dist_call)

initial.boot1 <- .get.initialvals(dat, j1, ndistparams, MLE.function, lower, upper,
dist, formals.dist)

opt.boot1 <- solnp(initial.boot1, fun = fmin.boot1, ineqfun = ineq.j1, ineqLB = 0,
ineqUB = 1, LB = lx.j1, UB = ux.j1, control = control)
opt.boot1\$pars <- .augment.pars(opt.boot1\$pars, j1)
hellinger.boot1 <- fmin.boot1(opt.boot1\$pars)

return(hellinger.boot0 - hellinger.boot1)

}

bt <- boot(dat, statistic = stat, R = B, sim = "parametric", ran.gen = ran.gen,
mle = Mix.boot, ...)
diff.boot <- bt\$t

q_lower <- quantile(diff.boot, probs = ql)
q_upper <- quantile(diff.boot, probs = qu)

if(diff.0 >= q_lower && diff.0 <= q_upper){
# so that the printed result reflects that the order j.max was actually estimated
# rather than just returned as the default
j.max <- j.max + 1
break
} else if (j0 == j.max){
break
}

}

.return.paramEst(j0, j.max, dat, theta.j0, values.j0, conv.j0, dist, ndistparams, formals.dist,
discrete, MLE.function)
}
```
anjaweigel/mixComp_package documentation built on Sept. 2, 2020, 3:55 p.m.