181,619 research outputs found
Robust Lorenz Curves: A Semiparametric Approach
Lorenz curves and second-order dominance criteria are known to be sensitive to data contamination in the right tail of the distribution. We propose two ways of dealing with the problem: (1) Estimate Lorenz curves using parametric models for income distributions, and (2) Combine empirical estimation with a parametric (robust) estimation of the upper tail of the distribution using the Pareto model. Approach (2) is preferred because of its flexibility. Using simulations we show the dramatic effect of a few contaminated data on the Lorenz ranking and the performance of the robust approach (2). Statistical inference tools are also provided.Welfare dominance, Lorenz curve, Pareto model, M-estimators.
Robust stochastic dominance: A semi-parametric approach
Lorenz curves and second-order dominance criteria, the fundamental tools for stochastic dominance, are known to be sensitive to data contamination in the tails of the distribution. We propose two ways of dealing with the problem: (1) Estimate Lorenz curves using parametric models and (2) combine empirical estimation with a parametric (robust) estimation of the upper tail of the distribution using the Pareto model. Approach (2) is preferred because of its flexibility. Using simulations we show the dramatic effect of a few contaminated data on the Lorenz ranking and the performance of the robust semi-parametric approach (2). Since estimation is only a first step for statistical inference and since semi-parametric models are not straightforward to handle, we also derive asymptotic covariance matrices for our semi-parametric estimator
Bayesian interpretation of Generalized empirical likelihood by maximum entropy
We study a parametric estimation problem related to moment condition models.
As an alternative to the generalized empirical likelihood (GEL) and the
generalized method of moments (GMM), a Bayesian approach to the problem can be
adopted, extending the MEM procedure to parametric moment conditions. We show
in particular that a large number of GEL estimators can be interpreted as a
maximum entropy solution. Moreover, we provide a more general field of
applications by proving the method to be robust to approximate moment
conditions
Modelling Lorenz Curves:robust and semi-parametric issues
Modelling Lorenz curves (LC) for stochastic dominance comparisons is central to the analysis of income distribution. It is conventional to use non-parametric statistics based on empirical income cumulants which are in the construction of LC and other related second-order dominance criteria. However, although attractive because of its simplicity and its apparent flexibility, this approach suffers from important drawbacks. While no assumptions need to be made regarding the data-generating process (income distribution model), the empirical LC can be very sensitive to data particularities, especially in the upper tail of the distribution. This robustness problem can lead in practice to 'wrong' interpretation of dominance orders. A possible remedy for this problem is the use of parametric or semi-parametric models for the datagenerating process and robust estimators to obtain parameter estimates. In this paper, we focus on the robust estimation of semi parametric LC and investigate issues such as sensitivity of LC estimators to data contamination (Cowell and Victoria-Feser 2002), trimmed LC (Cowell and Victoria-Feser 2006) and inference for trimmed LC (Cowell and Victoria-Feser 2003), robust semi-parametric estimation for LC (Cowell and Victoria-Feser 2007) selection of optimal thresholds for (robust) semi parametric modelling (Dupuis and Victoria-Feser 2006) and use both simulations and real data to illustrate these points.
Learning how to be robust: Deep polynomial regression
Polynomial regression is a recurrent problem with a large number of
applications. In computer vision it often appears in motion analysis. Whatever
the application, standard methods for regression of polynomial models tend to
deliver biased results when the input data is heavily contaminated by outliers.
Moreover, the problem is even harder when outliers have strong structure.
Departing from problem-tailored heuristics for robust estimation of parametric
models, we explore deep convolutional neural networks. Our work aims to find a
generic approach for training deep regression models without the explicit need
of supervised annotation. We bypass the need for a tailored loss function on
the regression parameters by attaching to our model a differentiable hard-wired
decoder corresponding to the polynomial operation at hand. We demonstrate the
value of our findings by comparing with standard robust regression methods.
Furthermore, we demonstrate how to use such models for a real computer vision
problem, i.e., video stabilization. The qualitative and quantitative
experiments show that neural networks are able to learn robustness for general
polynomial regression, with results that well overpass scores of traditional
robust estimation methods.Comment: 18 pages, conferenc
Nonparametric Estimation of Multi-View Latent Variable Models
Spectral methods have greatly advanced the estimation of latent variable
models, generating a sequence of novel and efficient algorithms with strong
theoretical guarantees. However, current spectral algorithms are largely
restricted to mixtures of discrete or Gaussian distributions. In this paper, we
propose a kernel method for learning multi-view latent variable models,
allowing each mixture component to be nonparametric. The key idea of the method
is to embed the joint distribution of a multi-view latent variable into a
reproducing kernel Hilbert space, and then the latent parameters are recovered
using a robust tensor power method. We establish that the sample complexity for
the proposed method is quadratic in the number of latent components and is a
low order polynomial in the other relevant parameters. Thus, our non-parametric
tensor approach to learning latent variable models enjoys good sample and
computational efficiencies. Moreover, the non-parametric tensor power method
compares favorably to EM algorithm and other existing spectral algorithms in
our experiments
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