SIMEXBoost {SIMEXBoost}

Boosting Method with SIMEX Correction for High-Dimensional Error-Prone Data

Description

This function aims to address variable selection and estimation for (ultra)high-dimensional data subject to covariate measurement error, which are particularly considered in ME_Data.

Usage

SIMEXBoost(Y,Xstar,zeta=c(0,0.25,0.5,0.75,1),B=500,type="normal",sigmae,Iter=100,
Lambda=0,Extrapolation="linear")

Arguments

Y

Responses in the dataset. If type is specified as "normal", "binary", or "poisson", then Y should be a n-dimensional vector; if type is given by "AFT-normal" or "AFT-loggamma", then Y should be a (n,2) matrix of interval-censored responses, where the first column is the lower bound of an interval-censored response and the second column is the upper bound of an interval-censored response.

Xstar

An (n,p) matrix of the error-prone covariates.

zeta

A sequence of values used in the procedure of the SIMEX method. A default sequence is given by c(0,0.25,0.5,0.75,1).

B

The number of repetition in the SIMEX method. The default value is 500.

type

type reflects the specification of regression models. "normal" means the linear regression model with the error term generated by the standard normal distribution; "binary" means the logistic regression model; "poisson" means the Poisson regression model. In addition, the accelerated failure time (AFT) model is also considered to fit length-biased and interval-censored survival data. Specifically, "AFT-normal" represents the AFT model with the error term being normal distributions; "AFT-loggamma" represents the AFT model with the error term specified as log-gamma distributions.

sigmae

An (p,p) covariance matrix of the noise term in the classical measurement error model.

Iter

The number of iterations for the boosting procedure. The default value is 100.

Lambda

A tuning parameter that aims to deal with the collinearity of covariates. Lambda=0 means that no L2-norm is involved, and it is taken as the default value.

Extrapolation

A extrapolation function for the SIMEX method. Two choices are included: "linear" means a linear function; "quadratic" means a quadratic function. The default argument is "linear".

Details

This function aims to address variable selection and estimation for (ultra)high-dimensional data subject to covariate measurement error. In the SIMEX method, inputs of B, zeta, and Extrapolation are user-specific. Normally, larger values of B and zeta give a more precise estimator, and meanwhile, longer computational times. More detailed descriptions of the SIMEX method can be found in the following references.

Value

BetaHatCorrect

the estimator obtained by SIMEXBoost.

Author(s)

Bangxu Qiu and Li-Pang Chen

References

Chen, L.-P. (2023). De-noising boosting methods for variable selection and estimation subject to error-prone variables. Statistics and Computing, 33:38.

Chen, L.-P. and Qiu, B. (2023). Analysis of length-biased and partly interval-censored survival data with mismeasured covariates. Biometrics. To appear. <doi: 10.1111/biom.13898>

Chen, L.-P. and Yi, G. Y. (2021). Analysis of noisy survival data with graphical proportional hazards measurement error models. Biometrics, 77, 956–969.

Hastie, T., Tibshirani, R. and Friedman, J. (2008). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York.

See Also

ME_Data Boost_VSE

Examples

##### Example 1: A linear model under default settings #####

X1 = matrix(rnorm((20)*400),nrow=400,ncol=20,byrow=TRUE)

data=ME_Data(X1,beta=c(1,1,1,rep(0,dim(X1)[2]-3)),
type="normal",
sigmae=diag(0.1,dim(X1)[2]))

Y = data$response
Xstar = data$ME_covariate

SIMEXBoost(Y,Xstar,B=2,zeta=c(0,0.5,1),
type="normal",Iter=3,sigmae=diag(0.1,dim(X1)[2]))



##### Example 2: An AFT model #####

X1 = matrix(rnorm((100)*400),nrow=400,ncol=100,byrow=TRUE)

data=ME_Data(X1,beta=c(1,1,1,rep(0,dim(X1)[2]-3)),pr0=0.3,
type="AFT-loggamma",
sigmae=diag(0.1,dim(X1)[2]))

Y = data$response
Xstar = data$ME_covariate

SIMEXBoost(Y,Xstar,B=2,zeta=c(0,0.5,1),
type="AFT-loggamma",Iter=3,sigmae=diag(0.1,dim(X1)[2]))