# TOHM-package: Testing One Hypothesis Multiple Times In TOHM: Testing One Hypothesis Multiple Times

## Description

Approximations of global p-values when testing hypothesis in presence of non-identifiable nuisance parameters. The method relies on the Euler characteristic heuristic and the expected Euler characteristic is efficiently computed by in Algeri and van Dyk (2018) <arXiv:1803.03858>.

## 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).

## Author(s)

Sara Algeri Maintainer: Sara Algeri <salgeri@umn.edu>

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35``` ```#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) ```

TOHM documentation built on March 10, 2021, 1:05 a.m.