Flexible Tweedie regression models for continuous data
By Wagner Hugo Bonat, Célestin C. Kokonendji. 2016
67 citations recorded by the source corpus.
ABSTRACT Tweedie regression models (TRMs) provide a flexible family of distributions to deal with non-negative right-skewed data and can handle continuous data with probability mass at zero. Estimation and inference of TRMs based on the maximum likelihood (ML) method are challenged by the presence of an infinity sum in the probability function and non-trivial restrictions on the power parameter space. In this paper, we propose two approaches for fitting TRMs, namely quasi-likelihood (QML) and pseudo-likelihood (PML). We discuss their asymptotic properties and perform simulation studies to compare our methods with the ML method. We show that the QML method provides asymptotically efficient estimation for regression parameters. Simulation studies showed that the QML and PML approaches present estimates, standard errors and coverage rates similar to the ML method. Furthermore, the second-moment assumptions required by the QML and PML methods enable us to extend the TRMs to the class of quasi-TRMs in Wedderburn's style. It allows to eliminate the non-trivial restriction on the power parameter space, and thus provides a flexible regression model to deal with continuous data. We provide an R implementation and illustrate the application of TRMs using three data sets.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/4b5582055e74ca7ec1c215b838d0ca49272c2c02
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In Artificial Intelligence
In Statistics and Probability
- Wagner Hugo Bonat
- Célestin C. Kokonendji
- John P. Hinde
- Clarice G. B. Dem'etrio
- Bent Jørgensen
- Dan Hall
Citations in the corpus
- Extended Poisson–Tweedie: Properties and regression models for count data (2016, methodology): “Bonat and Kokonendji (2017) showed in the context of Tweedie regression models that the quasi-score function provides asymptotically efficient estimators for the regression parameters; thus, a similar result is expected for the Poisson–Tweedie regression model.”