print: Dual Control Procedure

In JessieJeng/wsiHD: Weak Signal Inference Under High Dimensionality

Dual Control Procedure

Description

Implements a dual control method for signal selection.

Usage

fnpOpt(pval, pval_null, ...)

## S4 method for signature 'ANY,ANY'
fnpOpt(pval, pval_null, ...)

## S4 method for signature 'ANY,matrix'
fnpOpt(pval, pval_null, beta, alpha = 0.1)

## S4 method for signature 'ANY,big.matrix'
fnpOpt(pval, pval_null, beta, alpha = 0.1)

## S4 method for signature 'ANY,ff_matrix'
fnpOpt(pval, pval_null, beta, alpha = 0.1)

## S4 method for signature 'numeric,missingOrNull'
fnpOpt(pval, pval_null, beta, sHat)

## S4 method for signature 'matrix,missingOrNull'
fnpOpt(pval, pval_null, ...)

## S4 method for signature 'big.matrix,missingOrNull'
fnpOpt(pval, pval_null, beta, sHat)

## S4 method for signature 'ff_matrix,missingOrNull'
fnpOpt(pval, pval_null, ...)

## S4 method for signature 'ff_array,missingOrNull'
fnpOpt(pval, pval_null, ...)

## S4 method for signature 'ff_vector,missingOrNull'
fnpOpt(pval, pval_null, beta, sHat)

Arguments

pval	A numeric vector object, a big.matrix object with a single row or col, or an ff_vector, ff_array of single dimension, or ff_matrix with a single row or col p. The p-values. See Details.
pval_null	A numeric matrix object, a big.matrix object, or an ff_matrix object of dimension p x n. The p-values generated from the null distribution. The columns correspond to the samples (n), the rows to the signal variabless (p). If not provided (i.e., missing or), NULL) inputs c05 and c1 must be provided. If pval_null is provided, only input alpha is required. See Details.
...	Ignored.
beta	A numeric object. The threshold.
alpha	A numeric object. The significance level. The bounding sequence is estimated as the (1-alpha)-th quantile. This input is required only if pval_null is provided as input. See Details.
sHat	A numeric object. The estimated number of signal variables. This input is required only if pval_null is not provided as input. See Details.

Details

This function is multi-use in the sense that the algorithm depends on the combination of inputs provided. If inputs pval, beta, and sHat are provided, the function uses the provided estimated number of signals (sHat) to estimate the FNP. In contrast, if inputs pval, pval_null, beta, and alpha are provided, the function uses pval_null and alpha to estimate the number of signals, which is then used to estimate the FNP. This latter scenario is equivalent to calling cSeq(pval_null, alpha) to obtain c05 and c1, providing these as inputs to signalProp(pval, c05, c1) to obtain piHat, and then providing sHat = ceiling(p*piHat) as input to fnp(pval, beta, sHat).

The null p-values can be provided as a numeric matrix, a big.matrix as defined by the bigmemory package, or as an ff_matrix as defined by the ff package. The latter two options allow for larger matrices. Please see the documentation of these packages for details on creating objects.

The p-values can be provided as a numeric vector, a big.matrix with a single column or row, or as an ff object of class (ff_vector, ff_array of 1 dimension or ff_matrix with a single column or row). The latter two options allow for larger vectors.

Note that if both pval and pval_null are provided as input, they do not have to "match." For example pval can be a standard numeric vector with pval_null specified as a big.matrix.

If estimating the bounding sequence, note that the quantile() function of base R provides 9 algorithms for estimating the quantile, which are based on the definitions of Hyndman and Fan (1996). We have chosen the default (type = 7) here. However, the quantile algorithm implemented in Armadillo is type = 5 and that of ff is type = 1. Thus the results obtained using base, bigmemory, and ff objects containing equivalent data might differ slightly.

Value

An S3 object of class wsiHD comprising a list object. The exact contents depend on the input combination. The list will always include elements:

ind	The rank of the variables satisfying the threshold condition.
pvalue	The maximum p-value for variables satisfying the threshold condition.
FNP	A vector of the p FNP estimates. The class of this object will depend on the class of pval.

If the signal proportion is estimated internally, the list will also include

c05	Estimated bounding sequence when delta is set to the square root of the p-value.
c1	Estimated bounding sequence when delta is set equal to the p-value.
piHat	Estimated signal proportion.
piHat05	Estimated signal proportion when delta is set to the square root of the p-value.
piHat1	Estimated signal proportion when delta is set equal to the p-value.

References

Jeng, X. J. and Hu, Y (2021). Weak Signal Inference Under Dependence and Sparsity, submitted.

Examples

   data(wsiData)

   # limit data to expedite example
   smp <- sample(x = 2:4089, size = 500, replace = FALSE)

   Sigma <- stats::cor(x = wsiData[,smp])

   n <- 100L
   p <- ncol(x = Sigma)

   zz <- MASS::mvrnorm(n = n, mu = rep(x = 0.0, times = p), Sigma = Sigma)
   pval_null <- {1.0 - stats::pnorm(q = abs(x = zz))}*2.0

   pval <- stats::runif(n = p)

   cseq <- cSeq(pval_null = pval_null, alpha = 0.1)
   piHat <- signalProp(pval = pval, c05 = cseq$c05, c1 = cseq$c1)
   sHat <- ceiling(x = piHat$piHat*p)
   fnpOpt(pval = pval, beta = 0.1, sHat = sHat)

   # or equivalently obtained in one step as
   fnpOpt(pval = pval, pval_null = pval_null, alpha = 0.1, beta = 0.1)

JessieJeng/wsiHD documentation built on May 10, 2022, 12:33 a.m.