rcv {varEst}

Variance Estimation with Refitted Cross Validation(RCV)

Description

Estimation of error variance using Refitted cross validation in ultrahigh dimensional dataset.

Usage

rcv(x,y,a,d,method=c("spam","lasso","lsr"))

Arguments

x

a matrix of markers or explanatory variables, each column contains one marker and each row represents an individual.

y

a column vector of response variable.

a

value of alpha, range is 0<=a<=1 where, a=1 is LASSO penalty and a=0 is Ridge penalty. If variable selection method is LASSO then providing value to a is compulsory. For other methods a should be NULL.

d

number of variables to be selected from x.

method

variable selection method, user can choose any method among "spam", "lasso", "lsr"

Details

The error variance is estimated from a high dimensional datasets where number of parameters are more than number of individuals, i.e. p > n. Refitted cross validation method (RCV) which is a two step method, is used to get the estimate of the error variance. In first step, dataset is divided into two sub-datasets and with the help of Sparse Additive Models (SpAM) or LASSO or least squared regression (lsr) most significant markers(variables) are selected from the two sub-datasets. This results in two small sets of selected variables. Then using the set selected from 1st sub-dataset error variance is estimated from the 2nd sub-dataset with ordinary least square method and using the set selected from the 2nd sub-dataset error variance is estimated from the 1st sub-dataset with ordinary least square method. Finally the average of those two error variances are taken as the final estimator of error variance with RCV method.

Value

Error variance

Author(s)

Sayanti Guha Majumdar <[e-mail]>, Anil Rai, Dwijesh Chandra Mishra

References

Fan, J., Guo, S., Hao, N. (2012).Variance estimation using refitted cross-validation in ultrahigh dimensional regression. Journal of the Royal Statistical Society, 74(1), 37-65
Ravikumar, P., Lafferty, J., Liu, H. and Wasserman, L. (2009). Sparse additive models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(5), 1009-1030
Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of Royal Statistical Society, 58, 267-288

Examples

## data simulation
marker <- as.data.frame(matrix(NA, ncol =500, nrow = 200))
for(i in 1:500){
marker[i] <- sample(1:3, 200, replace = TRUE, prob = c(1, 2, 1))
}
pheno <- marker[,1]*1.41+marker[,2]*1.41+marker[,3]*1.41+marker[,4]*1.41+marker[,5]*1.41

pheno <- as.matrix(pheno)
marker<- as.matrix(marker)

## estimation of error variance
var <- rcv(marker,pheno,1,5,"spam")