Parametrically guided generalised additive models with application to mergers and acquisitions data

Abstract

Generalised nonparametric additive models present a flexible way to evaluate the effects of several covariates on a general outcome of interest via a link function. In this modelling framework, one assumes that the effect of each of the covariates is nonparametric and additive. However, in practice, often there is prior information available about the shape of the regression functions, possibly from pilot studies or exploratory analysis. In this paper, we consider such situations and propose an estimation procedure where the prior information is used as a parametric guide to fit the additive model. Specifically, we first posit a parametric family for each of the regression functions using the prior information (parametric guides). After removing these parametric trends, we then estimate the remainder of the nonparametric functions using a nonparametric generalised additive model and form the final estimates by adding back the parametric trend. We investigate the asymptotic properties of the estimates and show that when a good guide is chosen, the asymptotic variance of the estimates can be reduced significantly while keeping the asymptotic variance same as the unguided estimator. We observe the performance of our method via a simulation study and demonstrate our method by applying to a real data set on mergers and acquisitions.

Keywords:

• generalised additive model
• leveraged buyout
• local polynomial
• mergers and acquisitions
• parametric guide

Acknowledgements

Fan's research was partly supported by NSF grants DMS-0704337 and DMS-1206464. Maity's research was partly supported by NIH/NIEHS grant R00ES017744. Wu's research was partly supported by NSF grants DMS-0905561 and DMS-1055210. The content is solely the responsibility of the authors and does not necessarily represent the official views of NSF, NIH, or NIEHS. The authors are also grateful to two anonymous referees, one anonymous associate editor, and the editor for their careful evaluation of the paper and constructive comments that lead to a significantly improved version of the paper.

Additional information

Notes on contributors

Yihui Wang

On leave from Department of Finance, Chinese University of Hong Kong, Hong Kong.