Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS
Volume 61, Issue -, Pages 403-427Publisher
WILEY
DOI: 10.1111/j.1467-9876.2011.01033.x
Keywords
Generalized additive models for location; scale and shape; Gradient boosting; High dimensional data; Prediction inference; Spatial information; Variable selection
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Funding
- Interdisciplinary Center for Clinical Research at the University Hospital of the Friedrich-Alexander-Universitat Erlangen-Nurnberg [J11]
- Munich Center of Health Sciences
- German Research Foundation [HO 3242/1-3, KN 922/4-1]
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. Generalized additive models for location, scale and shape (GAMLSSs) are a popular semiparametric modelling approach that, in contrast with conventional generalized additive models, regress not only the expected mean but also every distribution parameter (e.g. location, scale and shape) to a set of covariates. Current fitting procedures for GAMLSSs are infeasible for high dimensional data set-ups and require variable selection based on (potentially problematic) information criteria. The present work describes a boosting algorithm for high dimensional GAMLSSs that was developed to overcome these limitations. Specifically, the new algorithm was designed to allow the simultaneous estimation of predictor effects and variable selection. The algorithm proposed was applied to Munich rental guide data, which are used by landlords and tenants as a reference for the average rent of a flat depending on its characteristics and spatial features. The net rent predictions that resulted from the high dimensional GAMLSSs were found to be highly competitive and covariate-specific prediction intervals showed a major improvement over classical generalized additive models.
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