Statistics and Its Interface

Volume 9 (2016)

Number 3

Nonlinear censored regression models with heavy-tailed distributions

Pages: 281 – 293

DOI: http://dx.doi.org/10.4310/SII.2016.v9.n3.a3

Authors

Aldo M. Garay (Department of Statistics, Campinas State University, Campinas, São Paulo, Brazil)

Victor H. Lachos (Department of Statistics, Campinas State University, Campinas, São Paulo, Brazil)

Tsung-I Lin (China Medical University, National Chung Hsing University, Taichung, Taiwan)

Abstract

In the framework of censored nonlinear regression models, the random errors are routinely assumed to have a normal distribution, mainly for mathematical convenience. However, this method has been criticized in the literature due to its sensitivity to deviations from the normality assumption. In practice, data such as income or viral load in AIDS studies, often violate this assumption because of heavy tails. In this paper, we establish a link between the censored nonlinear regression model and a recently studied class of symmetric distributions, which extends the normal one by the inclusion of kurtosis, called scale mixtures of normal (SMN) distributions. The Student-t, Pearson type VII, slash and contaminated normal, among others distributions, are contained in this class. Choosing a member of this class can be a good alternative to model this kind of data, because they have been shown its flexibility in several applications.We develop an analytically simple and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of model parameters together with standard errors as a byproduct. The algorithm uses nice expressions at the E-step, relying on formulae for the mean and variance of truncated SMN distributions. The usefulness of the proposed methodology is illustrated through applications to simulated and real data.

Keywords

censored nonlinear regression model, em-type algorithms, scale mixtures of normal distributions, outliers

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