ssa (version 1.3.0)

nfsdr2: Nonparametric false simultaneous discovery rate control, two thresholds

Description

Given two sequences of paired test statistics, returns the optimal rectangular rejection that identifies the largest number of simultaneous signals while controlling the false discovery rate. Allows different thresholds for each sequence.

Usage

nfsdr2(T1, T2, alpha, m1 = 10000, m2 = 10000, p1 = TRUE, p2 = TRUE,
  jitter = NULL)

Arguments

T1, T2

paired vectors of test statistics, both must be the same length; can be p-values or otherwise; if not p-values, must be stochastically larger under the null; must contain only positive values

alpha

nominal false simultaneous discovery rate

m1, m2

search only up the m1th (m2th) most significant test statistic in T1 (T2); NULL to search through all statistics

p1, p2

TRUE if T1 (T2) is a vector of p-values

jitter

NULL if no jittering is desired to resolve ties, otherwise a jitter of runif(0,jitter) will be added to all entries of T1 and T2

Value

two-component vector; the first component is the optimal threshold for T1 and the second is for T2

Examples

# NOT RUN {
## generate paired test statistics
p <- 10^6; ## total number of pairs
X <- c(rep(0,p-30),rep(1,10),rep(2,10),rep(3,10));
## X=0: no signal in either sequence of tests
## X=1: signal in sequence 1 only
## X=2: signal in sequence 2 only
## X=3: simultaneous signal
set.seed(1);
Z1 <- rnorm(p,0,1); Z1[X==1|X==3] <- rnorm(20,3,1);
Z2 <- rnorm(p,0,1); Z2[X==2|X==3] <- rnorm(20,4,1);
## convert to p-value
P1 <- 2*pnorm(-abs(Z1));
P2 <- 2*pnorm(-abs(Z2));
## run different version of fsdr()
out.pp <- fsdr(P1,P2,alpha=0.05);
out.zp <- fsdr(abs(Z1),P2,p1=FALSE,alpha=0.05);
out.pz <- fsdr(P1,abs(Z2),p2=FALSE,alpha=0.05);
out.zz <- fsdr(abs(Z1),abs(Z2),p1=FALSE,p2=FALSE,alpha=0.05);
## discovered simultaneous features
R1 <- which(P1<=out.pp[1]&P2<=out.pp[2]);
R2 <- which(abs(Z1)>=out.zp[1]&P2<=out.zp[2]);
R3 <- which(P1<=out.pz[1]&abs(Z2)>=out.pz[2]);
R4 <- which(abs(Z1)>=out.zz[1]&abs(Z2)>=out.zz[2]);
# }
# NOT RUN {
# }