doubconetest function

Test for a vector being in the null space of a double cone

Given an n-vector y and the model y=m+e, and an m by n "irreducible" matrix amat, test the null hypothesis that the vector m is in the null space of amat.

doubconetest(y, amat, nsim = 1000)

Arguments

• y: a vector of length n
• amat: an m by n "irreducible" matrix
• nsim: number of simulations to approximate null distribution -- default is 1000, but choose more if a more precise p-value is desired

Details

The matrix amat defines a polyhedral convex cone of vectors x such that amat%%x>=0, and also the opposite cone amat%%x<=0. The linear space C is those x such that amat%*%x=0. The function provides a p-value for the null hypothesis that m=E(y) is in C, versus the alternative that it is in one of the two cones defined by amat.

Returns

• pval: The p-value for the test

• p0: The least-squares fit under the null hypothesis

• p1: The least-squares fit to the "positive" cone

• p2: The least-squares fit to the "negative" cone

References

TBA, Meyer, M.C. (1999) An Extension of the Mixed Primal-Dual Bases Algorithm to the Case of More Constraints than Dimensions, Journal of Statistical Planning and Inference, 81, pp13-31.

Author(s)

Mary C Meyer and Bodhisattva Sen

See Also

agconst,partlintest

Examples

## test against a constant function
n=100
x=1:n/n
mu=4-5*(x-1/2)^2
y=mu+rnorm(n)
amat=matrix(0,nrow=n-1,ncol=n)
for(i in 1:(n-1)){amat[i,i]=-1;amat[i,i+1]=1}
ans=doubconetest(y,amat)
ans$pval
plot(x,y,col="slategray");lines(x,mu,lty=3,col=3)
lines(x,ans$p1,col=2)
lines(x,ans$p2,col=4)