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Estimation and diagnostic for skew-normal partially linear models

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  • Clécio S. Ferreira
  • Gilberto A. Paula

Abstract

Partially linear models (PLMs) are an important tool in modelling economic and biometric data and are considered as a flexible generalization of the linear model by including a nonparametric component of some covariate into the linear predictor. Usually, the error component is assumed to follow a normal distribution. However, the theory and application (through simulation or experimentation) often generate a great amount of data sets that are skewed. The objective of this paper is to extend the PLMs allowing the errors to follow a skew-normal distribution [A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178], increasing the flexibility of the model. In particular, we develop the expectation-maximization (EM) algorithm for linear regression models and diagnostic analysis via local influence as well as generalized leverage, following [H. Zhu and S. Lee, Local influence for incomplete-data models, J. R. Stat. Soc. Ser. B 63 (2001), pp. 111–126]. A simulation study is also conducted to evaluate the efficiency of the EM algorithm. Finally, a suitable transformation is applied in a data set on ragweed pollen concentration in order to fit PLMs under asymmetric distributions. An illustrative comparison is performed between normal and skew-normal errors.

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  • Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:16:p:3033-3053
    DOI: 10.1080/02664763.2016.1267124
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    Cited by:

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    3. Nicole Jeldes & Germán Ibacache-Pulgar & Carolina Marchant & Javier Linkolk López-Gonzales, 2022. "Modeling Air Pollution Using Partially Varying Coefficient Models with Heavy Tails," Mathematics, MDPI, vol. 10(19), pages 1-24, October.

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