A multiple testing procedure for clustered alternative hypotheses. It is assumed that the p-values under the null hypotheses follow U(0,1) and that the distributions of p-values from the alternative hypotheses are stochastically smaller than U(0,1). By aggregating information, this method is more sensitive to detecting signals of low magnitude than standard methods. Additionally, sporadic small p-values appearing within a null hypotheses sequence are avoided by averaging on the neighboring p-values.
changePoint(pvalues, alpha, km, lm, compare = "BOTH", fdrlWindow = 3,
fdrlNStep = 300, fdrlLambda = 0.1)an object of class numeric. A vector of p-values.
an object of class numeric. The significant level for the estimation of the critical value, gamma*.
an object of class numeric. The size of the window defining the neighborhood in left and right distances.
an object of class numeric. The size of the window defining the neighborhood in the long-run variance estimation.
one of ("FDRL", "BH", "Both", "None"). In addition to the Cao-Wu method, obtain significance indicators using the FDR_L method (FDRL) (Zhang et al., 2011), the Benjamini-Hochberg method (BH), (Benjamini andHochberg, 1995), "both" the FDRL and the BH methods, or do not consider alternative methods (none).
an object of class numeric. If FDR_L method requested, the size of the window defining the neighborhood.
an object of class numeric. If FDR_L method requested, the number of threshold values to consider.
and object of class numeric. If FDR_L method requested, the tuning constant.
Returns an object of class changePoint.
The comparison capability is included only for convenience and reproducibility of the original manuscript. The Benjamini-Hochberg and FDR_L methods cannot be accessed outside of the changePoint function.
The following methods retrieve individual results from a changePoint object, x:
BH(x):
Retrieves a vector of integer values.
An element is 1 if the null hypothesis is rejected
by the Benjamini-Hochberg (1995) method.
blocks(x):
Retrieves a list, each element of which is
a vector of integer values.
Each vector contains the indices of
an alternative hypothesis block.
CW(x):
Retrieves a vector of integer values.
An element is 1 if the null hypothesis is rejected
by the Cao-Wu change point (2015) method.
changePts(x):
Retrieves a vector of integer values.
The vector of change points identified by the
Cao-Wu (2015) method. If no change points are
identified, NULL is returned.
FDRL(x):
Retrieves a vector of integer values.
Elements are 1 if the null hypothesis is rejected
by the FDR_L (Zhang et al. 2011) method.
critical(x): Retrieves the
estimated critical value for testing used by
the Cao-Wu (2015) method.
numAlt(x): Retrieves the
estimated number of alternative hypotheses
obtained by the Cao-Wu (2015) method.
piAlt(x): Retrieves the
estimated proportion of alternative hypotheses
obtained by the Cao-Wu (2015) method.
plot(x, y, logp, ...): Generates plots
of -log(p) vs position or p-value vs position for
each alternative hypothesis block obtained
by the Cao-Wu (2015) method. logp is TRUE/FALSE
indicating if -log(p)/p-values are plotted on the y-axis.
sigmaSq(x): Retrieves the
estimated variance used to determine the critical value of
the Cao-Wu (2015) method.
Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57, 289--300.
Cao, H. and Wu, W. B. (2015) Changepoint estimation: Another look at multiple testing problems. Biometrika, 102, 974--980.
Zhang, C., Fan, J., and Yu, T. (2011). Multiple testing via FDRL for large-scale imaging data. Anals of Statistics, 39, 613--642.
# NOT RUN {
m <- 5000
T <- c(rep(0.1, 75), rep( 0.8, 75), rep(1.8, 100),
rep(0.0,2250), rep(-1.5,250), rep(0.0,2250)) +
rnorm(m, mean=0.0, sd = 1.0)
pv <- 2.0*(1.0-pnorm(abs(T)))
res <- changePoint(pvalues = pv,
alpha = 0.05,
km = {log(m)}^2,
lm = m^{1/4},
compare = "Both")
print(changePts(res))
print(head(cbind(BH(res),FDRL(res),CW(res))))
# }
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