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Graf, Monique

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Graf, Monique
Affiliation principale
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https://libra.unine.ch/handle/123456789/718

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  • Publication
    Métadonnées seulement
    A generalized mixed model for skewed distributions applied to small area estimation
    (2018-6-22)
    Graf, Monique 
    ;
    Marin, Juan Miguel
    ;
    Molina, Isabel
    Models with random (or mixed) effects are commonly used for panel data, in microarrays, small area estimation and many other applications. When the variable of interest is continuous, normality is commonly assumed, either in the original scale or after some transformation. However, the normal distribution is not always well suited for modeling data on certain variables, such as those found in Econometrics, which often show skewness even at the log scale. Finding the correct transformation to achieve normality is not straightforward since the true distribution is not known in practice. As an alternative, we propose to consider a much more flexible distribution called generalized beta of the second kind (GB2). The GB2 distribution contains four parameters with two of them controlling the shape of each tail, which makes it very flexible to accommodate different forms of skewness. Based on a multivariate extension of the GB2 distribution, we propose a new model with random effects designed for skewed response variables that extends the usual log-normal nested error model. Under this new model, we find empirical best predictors of linear and nonlinear characteristics, including poverty indicators, in small areas. Simulation studies illustrate the good properties, in terms of bias and efficiency, of the estimators based on the proposed multivariate GB2 model. Results from an application to poverty mapping in Spanish provinces also indicate efficiency gains with respect to the conventional log-normal nested error model used for poverty mapping.
  • Publication
    Métadonnées seulement
    Estimation of poverty indicators in small areas under skewed distributions
    (2014)
    Graf, Monique 
    ;
    Marin, Juan Miguel
    ;
    Molina, Isabel
    The standard methods for poverty mapping at local level assume that incomes follow a log-normal model. However, the log-normal distribution is not always well suited for modeling the income, which often shows skewness even at the log scale. As an alternative, we propose to consider a much more flexible distribution called generalized beta distribution of the second kind (GB2). The flexibility of the GB2 distribution arises from the fact that it contains four parameters in contrast with the two parameters of the log normal. One of the parameters of the GB2 controls the shape of left tail and another controls the shape of the right tail, making it suitable to model different forms of skewness. In particular, it includes the log-normal distribution as a limiting case. In this sense, it can be seen as an extension of the log-normal model to handle more adequately potential atypical or extreme values and it has been successfully applied to model the income. We propose a small area model for the incomes based on a multivariate extension of the GB2 distribution. Under this model, we define empirical best (EB) estimators of general non-linear area parameters; in particular, poverty indicators and we describe how to obtain Monte Carlo approximations of the EB estimators. A parametric bootstrap procedure is proposed for estimation of the mean squared error.