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Robledo, Kristy P.; Marschner, Ian C.

A new algorithm for fitting semi-parametric variance regression models. (English) Zbl 1505.62340

Comput. Stat. 36, No. 4, 2313-2335 (2021).
Summary: Variance regression allows for heterogeneous variance, or heteroscedasticity, by incorporating a regression model into the variance. This paper uses a variant of the expectation-maximisation algorithm to develop a new method for fitting additive variance regression models that allow for regression in both the mean and the variance. The algorithm is easily extended to allow for B-spline bases, thus allowing for the incorporation of a semi-parametric model in both the mean and variance. Although there are existing methods to fit these types of models, this new algorithm provides a reliable alternative approach that is not susceptible to numerical instability that can arise in this constrained estimation context. We utilise the developed algorithm with a series of simulation studies and analyse illustrative data. Various simulation studies show that the algorithm can recover the true model for a variety of scenarios. We also study automatic selection of model complexity based on information-based criteria, and show that the Akaike information criterion is useful for choosing the optimal number of knots in a B-spline model. An R package is available for implementing these methods.

MSC:

62-08 Computational methods for problems pertaining to statistics
62F10 Point estimation

Keywords:

variance regression; semiparametric regression; EM algorithm; B-splines

Software:

R; GLIM; MASS (R); VarReg; logbin; SemiPar
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\textit{K. P. Robledo} and \textit{I. C. Marschner}, Comput. Stat. 36, No. 4, 2313--2335 (2021; Zbl 1505.62340)
Full Text: DOI

References:

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