Inferential Aspects of the Skew Exponential Power Distribution

DiCiccio, Thomas J.; Monti, Anna Clara

doi:10.1198/016214504000000359

Cited by 101 publications

(84 citation statements)

References 12 publications

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“…This makes it natural to consider a Student's t distribution as an underlying joint distribution for the selection model. The robustness properties of the Student's t distribution (Lange et al 1989, Azzalini and Genton 2008, DiCiccio and Monti 2009) also make it an attractive parametric alternative to the normal distribution. For example, this distribution has been used recently to relax the assumption of normality in various statistical models such as censored regression (Muñoz-Gajardo et al 2010), treatment models (Chib and Hamilton 2000), and switching regression (Scruggs 2007), to name a few.…”

Section: Introductionmentioning

confidence: 99%

A Heckman Selection-tModel

Marchenko

Genton

2012

Journal of the American Statistical Association

104

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Sample selection arises often in practice as a result of the partial observability of the outcome of interest in a study. In the presence of sample selection, the observed data do not represent a random sample from the population, even after controlling for explanatory variables. That is, data are missing not at random. Thus, standard analysis using only complete cases will lead to biased results. Heckman introduced a sampleselection model to analyze such data and proposed a full maximum likelihood estimation method under the assumption of normality. The method was criticized in the literature because of its sensitivity to the normality assumption. In practice, data, such as income or expenditure data, often violates the normality assumption because of heavier tails. We first establish a new link between sample-selection models and recently studied families of extended skew-elliptical distributions. Then, this allows us to introduce a selection-t model, which models the error distribution using a Student's t distribution. We study its properties and investigate the finite-sample performance of the maximum likelihood estimators for this model. We compare the performance of the selection-t model to the conventional Heckman selection-normal model and apply it to analyze ambulatory expenditures. Unlike the selection-normal model, our analysis using the selection-t model provides statistical evidence for the existence of sample selection bias in these data. We also investigate the performance of the test for sample selection bias based on the selection-t model and compare it to the performances of several tests used with the selection-normal model. Our findings indicate that the latter tests can be misleading in the presence of heavy-tailed data.

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Section: Introductionmentioning

confidence: 99%

A Heckman Selection-tModel

Marchenko

Genton

2012

Journal of the American Statistical Association

104

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“…Examples of the former approach are DiCiccio and Monti (2004) for the EP, and Azzalini and Capitanio (2003) for the Student's t. Examples of the second approach are Fernández et al (1995), Theodossiou (2000), Komunjer (2007), and Zhu and Zinde-Walsh (2009) for the EP, and Fernández and Steel (1998), Bauwens and Laurent (2005), and Zhu and Galbraith (2010) for the t distribution ( Aas and Haff (2006) contains a brief review of different skewing approaches to the t distribution in finance). The main advantage of the Azzalini (1986) method is that it enables some elegant and attractive manipulation properties.…”

Section: Statistical Frameworkmentioning

confidence: 99%

Financial density selection

Marín

Sucarrat

2012

The European Journal of Finance

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We propose and study simple but flexible methods for density selection of skewed versions of the two most popular density classes in finance, the exponential power distribution and the t distribution. For the first type of method, which simply consists of selecting a density by means of an information criterion, the Schwarz criterion stands out since it performs well across density categories, and in particular when the Data Generating Process is normal. For the second type of method, General-to-Specific density selection, the simulations suggest that it can improve the recovery rate in predictable ways by changing the significance level. This is useful because it enables us to increase (reduce) the recovery rate of non-normal densities by increasing (reducing) the significance level, if one wishes to do so. The third type of method is a generalisation of the second type, such that it can be applied across an arbitrary number of density classes, nested or non-nested. Finally, the methods are illustrated in an empirical application. JEL Classification: C16, C52, C58Keywords: Financial returns, density selection, skewed exponential power distribution, skewed t distribution, general-to-specific density selection * We are thankful to Jonas Andersson, Mark Steel, and participants at the FIBE 2011 (Bergen) and CMS 2011 (Neuchatel) conferences for useful comments, suggestions and questions. We are also thankful for comments and suggestions on a precursor to this paper at the MAF 2010 conference (Ravello). Funding from The Bank of Spain Excellence Program is gratefully acknowledged.

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“…Innovating a complex error model such as in Schoups and Vrugt [2010] may ameliorate such concerns in practice. However, a simple model error that cannot be represented by the family of additive skew exponential power distributed [DiCiccio and Monti, 2004] error is sufficient to show the limitations of even such complex error models. For example, when the error due to model structure deficiency is correlated with model predictions [Pande et al, 2012a], it leads to an effect that is different from the heteroscedasticity effect.…”

Section: Introductionmentioning

confidence: 99%

“…This is because the assumptions on the error model structure define the likelihood function, which when valid yield the ''true'' parameter values of a hydrological model at the likelihood maximum. For example, Schoups and Vrugt [2010] assume that the error distribution belongs to a family of additive skew exponential power distribution [DiCiccio and Monti, 2004]. The method proposed in the paper makes no assumption on the structure of uncertainty due to underlying processes or measurement errors.…”

Section: Introductionmentioning

confidence: 99%

Quantile hydrologic model selection and model structure deficiency assessment: 1. Theory

Pande

2013

Water Resour. Res.

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[1] A theory for quantile based hydrologic model selection and model structure deficiency assessment is presented. The paper demonstrates that the degree to which a model selection problem is constrained by the model structure (measured by the Lagrange multipliers of the constraints) quantifies structural deficiency. This leads to a formal definition of model structure deficiency (or rigidity). Model structure deficiency introduces a bias in the prediction of an observed quantile, which is often not equal across quantiles. Structure deficiency is therefore diagnosed when any two quantile predictions for a given model structure cross since unequal bias across quantiles result in quantile predictions crossing. The analysis further suggests that the optimal value of quantile specific loss functions order different model structures by its structure deficiencies over a range of quantiles. In addition to such novelties, quantile hydrologic model selection is a frequentist approach that seeks to complement existing Bayesian approaches to hydrological model uncertainty.

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Inferential Aspects of the Skew Exponential Power Distribution

Cited by 101 publications

References 12 publications

A Heckman Selection-tModel

A Heckman Selection-tModel

Financial density selection

Quantile hydrologic model selection and model structure deficiency assessment: 1. Theory

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