TOHM (version 1.4)

TOHM-package: TOHM

Description

TOHM

Details

The functions collected in TOHM mainly focus on the implementation of the Likelihood Ratio Tests (see TOHM_LRT). However, several functions (e.g.,EC_T, global_p ) can be used to obtain global p-values for other test statistics and to compute the Euler characteristic using the graph algorithm described in Algeri and van Dyk (2018).

References

S. Algeri and D.A. van Dyk. Testing one hypothesis multiple times: The multidimensional case. arXiv:1803.03858, submitted to the Journal of Computational and Graphical Statistics, 2018.

Examples

# NOT RUN {
#generating data of interest
N<-100
x<-as.matrix(cbind(runif(N*2,172.5,217.5),runif(N*2,-2,58)))
x2<-x[(x[,1]<=217.5)&(x[,1]>=172.5),]
x_sel<-x2[(x2[,2]<=(28+sqrt(30^2-(x2[,1]-195)^2)))&(x2[,2]>=(28-
sqrt(30^2-(x2[,1]-195)^2))),]
data<-x_sel[sample(seq(1:(dim(x_sel)[1])),N),]

#Specifying minus-log-likelihood
kg<-function(theta){integrate(Vectorize(function(x) {
exp(-0.5*((x-theta[1])/0.5)^2)*integrate(function(y) {
exp(-0.5*((y-theta[2])/0.5)^2) }, 28-sqrt(30^2-(x-195)^2),
28+sqrt(30^2-(x-195)^2))$value}) , 172.5, 217.5)$value}
mll<-function(eta,x,theta){
  -sum(log((1-eta)/(pi*(30)^2)+eta*exp(-0.5*((x[,1]-
  theta[1])/0.5)^2-
  0.5*((x[,2]-theta[2])/0.5)^2)/kg(theta)))}

#Specifying search region
theta1<-seq(172.5,217.5,by=15)
theta2<-seq(-2,58,by=10)
THETA<-as.matrix(expand.grid(theta1,theta2))
originalR<-dim(THETA)[1]
rownames(THETA)<-1:(dim(THETA)[1])
THETA2<-THETA[(THETA[,1]<=217.5)&(THETA[,1]>=172.5),]
THETA_sel<-THETA2[(THETA2[,2]<=(28+sqrt(30^2-(THETA2[,1]-
195)^2)))&(THETA2[,2]>=(28-sqrt(30^2-(THETA2[,1]-195)^2))),]

#Generating toy EC
ECs<-cbind(rpois(100,1.5),rpois(100,1))

TOHM_LRT(data,mll,null0=0,init=c(0.1),lowlim=c(0),uplim=c(1),
THETA=THETA_sel,ck=c(1,8),type=c("Chi-bar^2"),
k=NULL,k_vec=c(0,1),weights=c(0.5,0.5),
ECdensities=NULL,ECs=ECs)
# }