StepwiseTest-package {StepwiseTest}

Multiple Testing Method to Control Generalized Family-Wise Error Rate and False Discovery Proportion

Description

Collection of stepwise procedures to conduct multiple hypotheses testing. The details of the stepwise algorithm can be found in Romano and Wolf (2007) <DOI:10.1214/009053606000001622> and Hsu, Kuan, and Yen (2014) <DOI:10.1093/jjfinec/nbu014>.

Usage

FWERkControl(test_stat, boot_stat, k, alpha)
FDPControl(test_stat, boot_stat, gamma, alpha)

Arguments

test_stat

m x 1 column vector of test statistics

boot_stat

m x B matrix of bootstrap statistics

k

Number of false rejections

gamma

False discovery proportion

alpha

The desired FWER(k) or FDP level

Value

Reject: A 0/1 numeric vector where the element j equals 1 indicates the model j is significant.

CV: The critical value.

Author(s)

Yu-Chin Hsu and Kendro Vincent

Maintainer: Kendro Vincent <[e-mail]>

References

Romano, J. P. and Wolf, M. (2005). “Stepwise multiple testing as formalized data snooping.” Econometrica, 73, 1237-1282.

Romano, J. P. and Wolf, M. (2007). “Control of generalized error rates in multiple testing.” Annals of Statistics, 35, 1378-1408.

Hsu, P.-H., Hsu, Y.-C., and Kuan, C.-M. (2010). “Testing the predictive ability of technical analysis using a new stepwise test without data-snooping bias.” Journal of Empirical Finance, 17, 471-484.

Hsu, Y.-C., Kuan, C.-M., and Yen, M.-F. (2014). “A generalized stepwise procedure with improved power for multiple inequalities testing.” Journal of Financial Econometrics, 12, 730-755.

Examples

# Specify the model parameters
m_null = 3
m_alt  = 7
m = m_null + m_alt
mu = c( rep(0, m_null), rep(0.5,m_alt) )
rho = 0.25
omega= (1-rho)*diag(1,m) + rho*matrix(1,m,m)
v=t(chol(omega))

# generate the data
n = 100
y = mu%*%matrix(1,1,n)+ v %*% matrix(rnorm(m*n),m,n)

# calculate the test statistics and bootstrap statistics
library(foreach)
library(tseries)
B = 100
y_mean = apply(y,1,mean)
y_sig = apply(y,1,sd)
t_stat = as.matrix(sqrt(n)*y_mean/y_sig)
s = tsbootstrap(1:n,B,b=2,type="stationary")
b_stat = foreach(i=1:B,.combine=cbind) %do% {
  y_boot = y[, s[,i]]
  y_mean_boot = apply(y_boot,1,mean)
  sqrt(n)*(y_mean_boot - y_mean)/y_sig
}

# Multiple test that controls FWER(1) at 5% significance level
FWERkControl(t_stat,b_stat,1,0.05)

# Multiple test that controls FWER(3) at 5% significance level
FWERkControl(t_stat,b_stat,1,0.05)

# Multiple test that controls FDP(0.1) at 5% significance level
FDPControl(t_stat,b_stat,0.1,0.05)