# Binary Generalized Extreme Value Additive Modelling

### Description

`bgeva`

provides a function for univariate modelling for binary rare events data with linear and nonlinear predictor effects when using the quantile function of the Generalized Extreme Value random variable.

### Details

`bgeva`

provides a function for flexible regression models for binary rare events data. The underlying representation and
estimation of the model is based on a penalized regression spline approach, with automatic smoothness selection. The
numerical routine carries out function minimization using a trust region algorithm from the package `trust`

in combination with
an adaptation of a low level smoothness selection fitting procedure from the package `mgcv`

.

`bgeva`

supports the use of many smoothers as extracted from `mgcv`

. Scale invariant tensor product smooths
are not currently supported. Estimation is by penalized maximum likelihood with automatic smoothness selection achieved
by using the approximate Un-Biased Risk Estimator (UBRE).

Confidence intervals for smooth components are derived using a Bayesian approach. Approximate p-values for testing
individual smooth terms for equality to the zero function are also provided. Functions `plot.bgeva`

and
`summary.bgeva`

extract such information from a fitted `bgevaObject`

. Variable
selection is also possible via the use of shrinakge smoothers or information criteria.

### Author(s)

Raffaella Calabrese (University of Milano-Bicocca, Department of Statistics and Quantitative Methods), Giampiero Marra (University College London, Department of Statistical Science) and Silvia Osmetti (University Cattolica del Sacro Cuore, Department of Statistics)

Maintainer: Giampiero Marra giampiero.marra@ucl.ac.uk

### References

Calabrese R., Marra G., Osmetti S.A. (2013), Bankruptcy Prediction of Small and Medium Enterprises Using a Flexible Binary Generalized Extreme Value Model. *Submitted*.

Calabrese R., Osmetti S.A. (2013), Modelling SME Loan Defaults as Rare Events: The Generalized Extreme Value Regression Model. *Journal of Applied Statistics*.

### See Also

`bgeva`