mvnData: Multivariate normal distribution data In GLSE: Graphical Least Square Estimation

Description

The function provides multivariate normal distribution data for regression purposes. It can generate predictors and a response at the same time or only predictors.

Usage

 `1` ```mvnData(sigma, n, mean, method = c("eigen", "svd", "chol"), sd = 1, Beta = NULL) ```

Arguments

 `sigma` A variance covariance matrix of dimension `v` x `v`. `n` The number of observations required to be generated. `mean` A vector of length `v`. `method` Possible methods are eigenvalue decomposition `"eigen"`, which is the default, singular value decomposition `"svd"`, and Cholesky decomposition `"chol"`. The method determines the matrix root of sigma. `sd` A vector of standard deviations of length `v`, which is only needed when the response is generated. `Beta` A vector of length `v`, which is only needed when the response is generated.

Value

A data frame consisting of

 `X ` The generated predictors. `Y ` The generated response if required.

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.

`mvtData`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```library(mvtnorm) # Generate sigma set.seed(1234) sigma <- matrix(0, nrow =5,ncol=5) sigma[1:5,1:5]<-.5 diag(sigma)<-3 # Generate vectors of Beta, mean and standard deviation Beta1<- round(runif(5,1.5,3.5),1) mu <- runif(5, 0, 0) sd <- runif(5, 1, 1) # Get the multivariate normal distribution data set.seed(123) result <-mvnData(sigma=sigma, n=10,mean=mu,sd=1,Beta=Beta1) result ```