# Robert B. Gramacy Associate Professor of Econometrics and Statistics

# Multivariate normal inference under monotone missingness

`monomvn`

is
an `R`

package for estimation of multivariate normal and
Student-t data of arbitrary dimension where the pattern of missing data is monotone.
Through the use of parsimonious/shrinkage regressions (plsr, pcr, lasso, ridge, etc.), where standard
regressions fail, the package can handle a nearly arbitrary amount of missing data.

This software is licensed under the GNU Lesser Public License (LGPL), version 2 or later. See the change log and an archive of previous versions.

The current version provides:

- maximum likelihood inference with optional penalties such as ridge, lasso, partial least squares, principal components, etc.
- Bayesian inference employing scale-mixture data augmentation
- A fully functional standalone interface to the Bayesian lasso (from Park & Casella), Normal-Gamma (from Griffin & Brown), Horseshoe (from Carvalho, Polson, & Scott), and ridge regression with model selection via Reversible Jump, and student-t errors (from Geweke).
- Monotone data augmentation extends the Bayesian approach to arbitrary missingness patterns.

## Obtaining the package

- Download
`R`

from cran.r-project.org by selecting the version for your operating system. - Install the
`monomvn`

,`pls`

and`lars`

packages, from within`R`

.

`R> install.packages(c("monomvn", "pls", "lars"))`

- Optionally, install the
`mvtnorm`

and`accuracy`

packages.

`R> install.packages(c("mvtnorm", "accuracy"))`

- Load the library as you would for any
`R`

library.

`R> library(monomvn)`

## Documentation

- See the package documentation.
A pdf
version of the reference manual, or help pages, is also available.
The help pages can be accessed from within
`R`

. Try starting with:`R> help(package=monomvn)`

`R> ?monomvn # follow the examples`

`R> ?bmonomvn # for a Bayesian version`

`R> ?blasso # for Bayesian lasso regression`

## References

- Gramacy, R.B., Pantaleo, E. (2009). Shrinkage regression for multivariate inference with missing data, and an application to portfolio balancing. Bayesian Analysis 5(2), pp. 237-262; preprint on arXiv:0907.2135
- Gramacy, R.B., Lee JH. (2007).
*On estimating covariances between many assets with histories of highly variable length*. arXiv:0710.5837 - Roderick J.A. Little and Donald B. Rubin (2002). Statistical Analysis with Missing Data, Second Edition. Wilely.
- Bjorn-Helge Mevik and Ron Wehrens (2007).
The
`pls`

Package: Principal Component and Partial Least Squares Regression in`R`

. Journal of Statistical Software**18**(2) - Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2003).
Least Angle Regression (with discussion). Annals of Statistics
**32**(2) - Park, T., Casella, G. (2008).
The Bayesian Lasso.
Journal of the American Statistical Association
**103**(482), pp. 681-686(6) - Griffin, J.E., Brown, P.J. (2009) Inference with Normal-Gamma prior distributions in regression problems. Bayesian Analysis, 5(1), pp. 171-188
- Carvalho, C.M., Polson, N.G., and Scott, J.G. (2010) The horseshoe estimator for sparse signals. Biometrika 97(2): pp. 465-480.
- Geweke, J. (1996). Variable selection and model comparison in regression. In Bayesian Statistics 5. Editors: J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith, 609-620. Oxford Press.
- Trevor Hastie, Robert Tibshirani and Jerome Friedman (2002).
*Elements of Statistical Learning.*Springer, NY. - Some of the code for
`monomvn`

, and its subroutines, was inspired by code written by Daniel Heitjan.