LCTnorm {TestCor}

Procedure LCT-N proposed by Cai & Liu (2016) for correlation testing.

Description

Procedure LCT-N proposed by Cai & Liu (2016) for correlation testing.

Usage

LCTnorm(
  data,
  alpha = 0.05,
  stat_test = "2nd.order",
  vect = FALSE,
  arr.ind = FALSE
)

Arguments

data

matrix of observations

alpha

level of multiple testing

stat_test

'empirical'

\sqrt{n}*abs(corr)

'fisher'

\sqrt{n-3}*1/2*\log( (1+corr)/(1-corr) )

'student'

\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)

'2nd.order'

\sqrt{n}*mean(Y)/sd(Y) with Y=(X_i-mean(X_i))(X_j-mean(X_j))

vect

if TRUE returns a vector of TRUE/FALSE values, corresponding to vectorize(cor(data)); if FALSE, returns an array containing TRUE/FALSE values for each entry of the correlation matrix

arr.ind

if TRUE, returns the indexes of the significant correlations, with respect to level alpha

Value

Returns

• logicals, equal to TRUE if the corresponding element of the statistic vector is rejected, as a vector or a matrix depending of the value of vect,

• an array containing indexes \lbrace(i,j),\,i<j\rbrace for which correlation between variables i and j is significant, if arr.ind=TRUE.

References

Cai, T. T., & Liu, W. (2016). Large-scale multiple testing of correlations. Journal of the American Statistical Association, 111(513), 229-240.

See Also

ApplyFdrCor, LCTboot

Examples

 
n <- 100
p <- 10
corr_theo <- diag(1,p)
corr_theo[1,3] <- 0.5
corr_theo[3,1] <- 0.5
data <- MASS::mvrnorm(n,rep(0,p),corr_theo)
alpha <- 0.05
# significant correlations:
LCTnorm(data,alpha,stat_test='empirical',arr.ind=TRUE)