BcorSIS {MFSIS}

A Generic Sure Independence Screening Procedure

Description

A generic nonparametric sure independence screening procedure, called BCor-SIS, on the basis of a recently developed universal dependence measure: Ball correlation. We show that the proposed procedure has strong screening consistency even when the dimensionality is an exponential order of the sample size without imposing sub-exponential moment assumptions on the data.

Usage

BcorSIS(X, Y, nsis = (dim(X)[1])/log(dim(X)[1]))

Arguments

X

The design matrix of dimensions n * p. Each row is an observation vector.

Y

The response vector of dimension n * 1. For survival models, Y should be an object of class Surv, as provided by the function Surv() in the package survival.

nsis

Number of predictors recruited by BcorSIS. The default is n/log(n).

Value

the labels of first nsis largest active set of all predictors

Author(s)

Xuewei Cheng [e-mail]

References

Pan, W., X. Wang, H. Zhang, H. Zhu, and J. Zhu (2020). Ball covariance: A generic measure of dependence in banach space. Journal of the American Statistical Association 115(529),307–317.

Pan, W., X. Wang, W. Xiao, and H. Zhu (2019). A generic sure independence screening procedure. Journal of the American Statistical Association 114(526), 928–937.

Examples

## Scenario 1  generate complete data
n <- 100
p <- 200
rho <- 0.5
data <- GendataLM(n, p, rho, error = "gaussian")
data <- cbind(data[[1]], data[[2]])
colnames(data)[1:ncol(data)] <- c(paste0("X", 1:(ncol(data) - 1)), "Y")
data <- as.matrix(data)
X <- data[, 1:(ncol(data) - 1)]
Y <- data[, ncol(data)]
A1 <- BcorSIS(X, Y, n / log(n))
A1

## Scenario 2  generate survival data
library(survival)
n <- 100
p <- 200
rho <- 0.5
data <- GendataCox(n, p, rho)
data <- cbind(data[[1]], data[[2]], data[[3]])
colnames(data)[ncol(data)] <- c("status")
colnames(data)[(ncol(data) - 1)] <- c("time")
colnames(data)[(1:(ncol(data) - 2))] <- c(paste0("X", 1:(ncol(data) - 2)))
data <- as.matrix(data)
X <- data[, 1:(ncol(data) - 2)]
Y <- Surv(data[, (ncol(data) - 1)], data[, ncol(data)])
A2 <- BcorSIS(X, Y, n / log(n))
A2