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Robust likelihood methods based on the skew-\(t\) and related distributions. (English) Zbl 1206.62102
Summary: The robustness problem is tackled by adopting a parametric class of distributions flexible enough to match the behaviour of the observed data. In a variety of practical cases, one reasonable option is to consider distributions which include parameters to regulate their skewness and kurtosis. As a specific representative of this approach, the skew-\(t\) distribution is explored in more detail and reasons are given to adopt this option as a sensible general-purpose compromise between robustness and simplicity, both of treatment and of interpretation of the outcome. Some theoretical arguments, outcomes of a few simulation experiments and various wide-ranging examples with real data are provided in support of the claim.

MSC:
62H10 Multivariate distribution of statistics
62H12 Estimation in multivariate analysis
65C05 Monte Carlo methods
62P05 Applications of statistics to actuarial sciences and financial mathematics
Software:
R; sn
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