lrm.dpd: MDPDE for Linear Regression Model with knwon error variance...

In abhianik/dpdSIS: Robust Variable Screening with DPD-SIS and DPD-CSIS

MDPDE for Linear Regression Model with knwon error variance (equal to one)

Description

Computes the robust Minimum Density Power Divergence Estimator (MDPDE) under a Linear Regression Model y=X*beta + e, with e ~ N(0, 1).

Usage

lrm.dpd(y, X, alpha, method = "L-BFGS-B", p = ncol(X), Initial = matrix(rep(1, p)))

Arguments

y	Vector. The response vector [n X 1].
X	Matrix. Covariate Matrix [n X p].
alpha	Numeric. The DPD tuning parameter (0<= alpha <=1)
p	Integer. Number of columns in the covariate matrix (X). Optional.
Initial	Vector. Initial values of the parameters for the estimation process (initial of sigma needs to be given via log(sigma)). Optional. Default is 1 for all slope parameters, median of y for intercept and MAD(y) for sigma.
Method	String. Numerical optimization method to be used for the estimation process. Possible options are "L-BFGS-B","Nelder-Mead", "BFGS", "CG", which are the same as the input of 'optim' function in R. Optional. Default is "L-BFGS-B".

Details

Reference: Ghosh, A., & Basu, A. (2013). Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression. Electronic Journal of statistics, 7, 2420-2456.

Value

A List of two elements. The first list element is a [p X 1] vector containing the parameter estimates. The second list element is an indicator if the numerical optimization within the estimation process has converged: 0 == convergence. (Same as the convergence from 'optim' function of R)

Examples

n <- 50; p <- 5;
beta <- rep(1,p); sigma<-1
SigmaX <- diag(p-1);
X <- mvrnorm(n, mu=rep(0,p-1), Sigma=SigmaX);
X0 <- cbind(1,X)
Y <- drop(X0 %*% beta + sigma*rnorm(n))

alpha <- 0.3
MDPDE<-lmr.dpd(Y,X0,alpha)

abhianik/dpdSIS documentation built on Sept. 5, 2022, 12:40 p.m.