GLSE (version 0.1.0)

GLSE: Graphical least square estimation

Description

The function estimates linear regression via graphical models in an unbiased way. This function aims to deal with studies where all covariates need to be kept in the model (such as portfolio optimisation), when the sample size is much less than covariate numbers. It supports both serial and parallel computations. However, the available computational resources should be considered before choosing one of the two options. For any given data, an estimated graph, regression parameters and errors are returned.

Usage

GLSE(x, y, centering = TRUE, lambda = 0, parallel = FALSE, clusters = NULL, c.size = NULL)

Arguments

x

A matrix of n x v dimension consisting of the predictors' values.

y

A response vector of length n.

centering

If equal to TRUE, then all the variables in x and the response y are centered. The default is TRUE.

lambda

The amount of regularisation for shrinking the graph. The default is 0.

parallel

Logical.Whether or not to do parallel computation. If set to TRUE, then clusters must also be provided. The default is FALSE.

clusters

The number of child nodes that must be created in the cluster if the parallel option is set to TRUE.

c.size

The allowed size of the clique (should not be greater than n). The default is n.

Value

A list of three values:

Graph

The estimated graph for the given data.

Beta

The vector of estimated regression parameters based on the estimated graph.

SSE

Sum of squares of errors for the parameters.

SE

Estimated standard errors for the parameters.

Details

The parallel options also work for Windows. Care should be taken in creating the cluster as all types of clusters do not work for Windows, e.g. FORK.

References

Alan, G. Frank, B. (2009), Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195., Springer-Verlag, Heidelberg. ISBN 978-3-642-01688-2.

Alan, G. Frank, B. Tetsuhisa, M. Xuefe, M. Friedrich, L. Fabian, S. and Torsten, H. (2019). mvtnorm: Multivariate Normal and t Distributions. R package version 1.0-7. URL http://CRAN.R-project.org/package=mvtnorm.

Aldahmani, S. and Dai, H. (2015). Unbiased Estimation for Linear Regression When n< v. International Journal of Statistics and Probability, 4(3), p61.

Csardi, G., and Nepusz, T. (2006). The igraph software package for complex network research. InterJournal, Complex Systems, 1695(5), 1-9.

Dethlefsen, C., and H?jsgaard, S. (2005). A common platform for graphical models in R: The gRbase package. Journal of Statistical Software, 14(17), 1-12.

See Also

BootSE

Examples

# NOT RUN {
###################################

# Example with serial processing.

###################################
library(gRbase)
library(igraph)
#load the data
data(qsbralks)
x <- as.matrix(qsbralks[,1:15])
y <- as.matrix(qsbralks[,22])

# Get the graph

# Call GLSE(.) .

results <- GLSE(x,y,parallel=FALSE)


# The returned objects are

results$Graph
results$Beta
results$SSE
results$Error

# Call plotG(.).

 plotG(results$Graph)
###################################

# Example with parallel processing.

###################################
library(gRbase)
library(igraph)
library(parallel)
#load the data
data(qsbralks)
x <- qsbralks[,1:15]
y <- qsbralks[,22]

# Create cluster

cl <- makeCluster(2)

# Send the gRbase package to all the nodes

clusterEvalQ(cl, library(gRbase))


# Call GLSE(.) .

results <- GLSE(x,y,parallel=TRUE,clusters=cl)

# Stop the cluster

stopCluster(cl)

# The returned objects are

results$Graph;
results$Beta;
results$SSE;
results$Error;

# Call plotG(.) .

plotG(results$Graph)


# }