# Estimation for multivariate normal data with monotone missingness (`monomvn` `R` package)

07/08/2011

`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.
The current version supports

- maximum likelihood inference with optional penalties such as ridge, lasso, partial least squares, principal components, etc.
- Bayesian inference employing scale-mixtures sampling under priors listed below ...
- 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.

This software is licensed under the GNU Lesser Public
License (LGPL), version 2 or later. See the
change
log.

## Obtaining `monomvn`

- Obtain
`R`from cran.r-project.org by selecting the version for your operating system. - Install the
`monomvn`,`pls`and`lars`packages, from within`R`.`> install.packages(c("monomvn", "pls", "lars"))` - Optionally, install the
`mvtnorm`and`accuracy`packages.`> install.packages(c("mvtnorm", "accuracy"))` - Load the library as you would for any
`R`library.`> library(monomvn)`

## Documentation

- See the package documentation. A pdf version of the
reference manual, or help pages, as also available.
The help pages can be accessed from within
`R`. Try starting with...`> help(package=monomvn)`

> ?monomvn # follow the examples

> ?bmonomvn # for a Bayesian version

> ?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.

## Please send questions and comments to rbgramacy_AT (_chicagobooth_DOT_edu). Enjoy!

*Robert B. Gramacy -- 2011*